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From: cipolla@sbu.ac.uk
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Bivariate Garch
Date: Tue, 6 Jun 2000 11:26:34 +0000
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Dear Rats users,
I am estimating a bivariate GARCH model, by using Rob 
Trevor code. I am trying to modify it by allowing for errors with a 
GED or t-student distribution, but I get as an error message: "failed 
to invert the covariance matrix, trying the generalised inverse". 
For some dataset  the generalised inversion procedure works, and I 
can compute point estimates and standard errors. For  other dataset, 
the generalised inversion procedure does not work: I end up with NA
standard errors and NA saved residuals. Does anyone have a code which 
allows for errors with GED or t-distribution distributions?
Many thanks
Andrea Cipollini
Andrea Cipollini
South Bank University
Business School
Southwark Campus
103 Borough Road
London SE1 0AA

Direct Line: +44 (0)171-8157077
E-mail: cipolla@sbu.ac.uk


---------- End of message ----------

From: "Estima" <tomm@estima.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Bivariate Garch
Date: Tue, 6 Jun 2000 09:46:04 -0500
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On 6 Jun 00, at 11:26, cipolla@sbu.ac.uk wrote:

> Dear Rats users,
> I am estimating a bivariate GARCH model, by using Rob 
> Trevor code. I am trying to modify it by allowing for errors with a 
> GED or t-student distribution, but I get as an error message: "failed 
> to invert the covariance matrix, trying the generalised inverse". 
> For some dataset  the generalised inversion procedure works, and I 
> can compute point estimates and standard errors. For  other dataset, 
> the generalised inversion procedure does not work: I end up with NA
> standard errors and NA saved residuals. Does anyone have a code which 
> allows for errors with GED or t-distribution distributions?

Andrea:

I don't think you are likely to find a "better" implementation of 
these models--the parameterizations in that example program are 
correct as far as I know. Rather, the problem you are experiencing 
most likely has to do with the initial conditions you are using 
(although there is always the possibility that your model simply 
doesn't fit the data). Thus the only likely improvement would be a 
method that produces better initial values for your particular 
model(s).

If you haven't already done so, be sure to include the TRACE option 
on your MAXIMIZE statement. This is always a good practice, but is 
vital in this case, because you need to determine which iterations 
are producing the "Non-invertible" warning message.

If you're just getting "Non-invertible" warnings on a few early 
iterations, but then things proceed smoothly (i.e. no such warnings 
on later iterations and the parameters/function value seem to 
converge nicely), then you are probably fine--the program has 
successfully moved away from bad initial conditions to an area where 
the model and parameter values produce valid covariance matrices. 
Obviously you'll want to experiment with some slightly different 
initial conditions to verify your results.

If, on the other hand, you are seeing these warnings at later 
iterations (i.e. at or shortly before the last iteration performed), 
then any results you might get are probably meaningless--even if you 
don't get NA's for your coefficients (you need the covariance matrix 
to be invertible). You'll need to go back to the drawing board in 
terms of your initial guesses for the parameters. Possibly try a 
simpler model first to get a better idea of what to expect, etc.

Sincerely,
Tom Maycock
Estima



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From: Lana Poukliakova <Lanapouk@excite.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: GARCHM with MA
Date: Tue, 6 Jun 2000 14:27:13 -0700 (PDT)
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Dear RATS users,
This is my third message already. I am a new user of RATS and I try to
estimate three variable GARCHM process with two moving averages. Can I use
available codes form the website for two variables and change them? How can
one possibly include MA in the program for GARCHM?
Thanks in advance.
Lana,
University of Alberta, Canada 





_______________________________________________________
Get 100% FREE Internet Access powered by Excite
Visit http://freelane.excite.com/freeisp


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From: Yuen Phui Ling Hazel <fbap8383@nus.edu.sg>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: DISPLAY OF RESIDUALS CORRELATION
Date: Fri, 9 Jun 2000 12:59:27 +0800 
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		Hi everyone,

		Does someone know how to display the correlations of
residuals/ errors of a VAR system? 

		Thanks very much. 

		Have a Nice day. 
		Hazel  

		 
				 -----Original Message-----
				From: 	Yuen Phui Ling Hazel  
				Sent:	Tuesday, May 02, 2000 7:37 PM
				To:	'RATS-L@EFS.MQ.EDU.AU'
				Subject:	VMA Syntax
				Importance:	High

				Does anyone know the VMA syntax and
procedure in RATS, apart from the one posted on the web?


				Hazel 	   fbap8383@nus.edu.sg
				University of Singapore 

---------- End of message ----------

From: =?iso-8859-1?q?Andreas=20Faust?= <andreasfaust@yahoo.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: DISPLAY OF RESIDUALS CORRELATION
Date: Fri, 9 Jun 2000 05:29:56 -0700 (PDT)
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
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Hi Hazel,
if you will use finally the VAR.SRC you have the
possibilty to see the correlation/error after
estimation. Also you can display the ACF of the
residulas. Try it!

Andreas


--- Yuen Phui Ling Hazel <fbap8383@nus.edu.sg>
schrieb: >=20
> 		Hi everyone,
>=20
> 		Does someone know how to display the correlations
> of
> residuals/ errors of a VAR system?=20
>=20
> 		Thanks very much.=20
>=20
> 		Have a Nice day.=20
> 		Hazel =20
>=20
> 		=20
> 				 -----Original Message-----
> 				From: 	Yuen Phui Ling Hazel =20
> 				Sent:	Tuesday, May 02, 2000 7:37 PM
> 				To:	'RATS-L@EFS.MQ.EDU.AU'
> 				Subject:	VMA Syntax
> 				Importance:	High
>=20
> 				Does anyone know the VMA syntax and
> procedure in RATS, apart from the one posted on the
> web?
>=20
>=20
> 				Hazel 	   fbap8383@nus.edu.sg
> 				University of Singapore=20


=3D=3D=3D=3D=3D
Andreas Faust
Av. Car=FApano N=B0 23
Qta. El Rosedal
Las Palmas, Caracas
Venezuela
Tel.: +58  2 7818621
andreasfaust@yahoo.com

__________________________________________________
Do You Yahoo!?
Yahoo! Photos -- now, 100 FREE prints!
http://photos.yahoo.com

---------- End of message ----------

From: "Estima" <tomm@estima.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: DISPLAY OF RESIDUALS CORRELATION
Date: Fri, 9 Jun 2000 10:18:59 -0500
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
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> 		Hi everyone,
> 
> 		Does someone know how to display the correlations of
> residuals/ errors of a VAR system? 
> 

Just use the SIGMA option on ESTIMATE if you want to see the 
covariance and correlation information for the residuals:

ESTIMATE(OUTSIGMA=V,sigma)

You can use CMOM(CORR) on the set of residuals series:

SYSTEM 1 TO NEQN
VARIABLES  USARGNP CANTBILL CANM1S CANRGNP CANCPINF CANUSXSR  LAGS 1 
TO NLAGS
DET CONSTANT
END(SYSTEM)

dec vec[series] resids(neqn)

ESTIMATE(OUTSIGMA=V,sigma) / resids(1)

cmom(corr,print) 
# resids

Sincerely,
Tom Maycock
Estima

--
------------------------------------------------------------
|   Estima                    |  Sales:   (800) 822-8038   |
|   P.O. Box 1818             |           (847) 864-8772   |
|   Evanston, IL 60204-1818   |  Support: (847) 864-1910   |
|   USA                       |  Fax:     (847) 864-6221   |
|   http://www.estima.com     |  estima@estima.com         |
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---------- End of message ----------

From: "Ana Timberlake" <info@timberlake.co.uk>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Newsflash: Special Offers on Training
Date: Fri, 09 Jun 2000 19:35:30 +0100
Errors-to: <rats-l-owner@efs.mq.edu.au>
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Dear Colleague

As a user of statistical packages, you may be interested in the news belo=
w. For=20
full details of our products, training courses and other services http://=
www.timberlake.co.uk=20
or http://www.timberlake-consultancy.com


CONTENTS
1. Training courses in the USA
2. Internet Training courses (SPECIAL OFFER)
3. Visit our stands at conferences (SPECIAL OFFER)
4. A new course: QUANTITATIVE METHODS IN FINANCIAL ECONOMICS: The Stock M=
arket,=20
the Bond Market and the Foreign Exchange Market, 26 - 29 September 2000, =
University=20
of London Computer Centre (ULCC), 20 Guilford Street, London WC1N 1DZ, UK.
5. Gauss version 3.5

1. Training courses in the USA
In addition to distribute third-party statistical and econometric softwar=
e, we=20
aim to provide the user, in addition to our technical support, with a var=
iety=20
of training courses. In the U.S.A. we are offering the following courses/=
workshops=20
:

We are offering 4 workshops before/after the World Conference of the Econ=
ometric=20
Society, 11 - 16 August 2000, Seattle,  U.S.A. During the workshops, the =
delegates=20
have access to computers so that they gain hands-on experience in the sof=
tware.=20
The price of the 1-day workshop is  245 USD and the 1/2 day workshop is 1=
75 USD.=20
The titles for the workshops, dates and names of the lecturers can be fou=
nd below.

- Modelling Dynamic Econometric Systems Using PcGive, Principal lecturer:=
 Prof.=20
David F. Hendry,1-day workshop, 10 August 2000, Seattle, U.S.A.
- Ox Course: An Introduction to Modern Econometric Programming, Principal=
 lecturers:=20
Jurgen Doornik and Marius Ooms, 1-day workshop, afternoon of 16 August & =
morning=20
of 17 August 2000, Seattle, U.S.A.
- STAMP 6: Structural time series analyser modeller and predictor
Principal lecturers: Prof. Andrew Harvey and Siem Jan Koopman, 1-day work=
shop,=20
10  August 2000, Seattle, U.S.A.
- Modelling Markov Switching Processes Using MSVAR for Ox, Principal lect=
urer:=20
Hans-Martin Krolzig, 1/2 day workshop, 17 afternoon, August 2000, Seattle=
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U.S.A.

In addition we are also organising a 4-day course in New York, 7-10 Novem=
ber=20
2000

- The Practice of Econometrics with EViews, Principal lecturers: Sean Hol=
ly and=20
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Details at www.timberlake.co.uk

2. Internet Training courses
We run several Internet courses during the year. All courses are four ses=
sions=20
and the price is: 150 GBP, 245 USD or 240 Euros. Register in 2 or more co=
urses=20
before 1st July 2000 and you will get 20% discount on the total cost of c=
ourses=20
- mention in your order OFFER INT JULY2000. These are some of the courses=
:

- Introduction to Medical Statistics with Stata - 19/Jun - 28/Jul/2000 		=
	=09
- Advanced Medical Statistics with Stata - 2/Oct- 10/Nov/2000 			=09
- Sample Size Calculations - 13/Nov - 15/Dec/2000			=09
- An Introduction to Time Series using Stata - 4/Sep - 13/Oct/2000
- Meta-analysis techniques using Stata - 6/Nov - 15/Dec/2000				=09
- Panel Data Analysis using Stata - 25/Sept - 3/Nov/2000=09
- Statistical Quality Control with Statgraphics - 4/Sept - 13/Oct/2000			=
=09

3. Visit our stands at conferences
We will be present at various conferences. Please visit us. We offer spec=
ial=20
prices for some of the software packages and training courses during thes=
e conferences.=20
If you order software prior to the conference and collect it at the confe=
rence,=20
you get a 15% discount. E-mail us conf@timberlake.co.uk to discuss your o=
rder.=20
You will also be saving the shipping costs. Please contact us 3 weeks pri=
or to=20
the start of the conference.

- The 20th International Symposium on Forecasting, Lisbon, Portugal, 21-2=
6 June=20
2000
- CEF2000 Sixth International Conference of the Society for Computation E=
conomics,=20
Barcelona, Spain, 6-8 July 2000
- Third European Congress of Mathematics, Barcelona, Spain, 10 - 14 July =
2000
- World Conference of the Econometric Society, Seattle, USA, 11 -16 Augus=
t 2000
- COMDEX Brazil 2000, Sao Paulo, Brazil, 22-25 August 2000
- International conference of the Royal Statistical Society,  Reading, UK=
, 11-15=20
September 1000
- VII Annual Conference of the Sociedade Portuguesa de Estat=EDstica, Pen=
iche,=20
Portugal, 4 - 7 October 2000
- Annual meeting of the American Economics Association, New Orleans, U.S.=
A.,=20
5-7 January 2000

4. A new course: QUANTITATIVE METHODS IN FINANCIAL ECONOMICS: The Stock M=
arket,=20
the Bond Market and the Foreign Exchange Market, 26 - 29 September 2000, =
University=20
of London Computer Centre (ULCC), 20 Guilford Street, London WC1N 1DZ, UK.

This course aims to provide delegates with a background to econometric mo=
delling=20
methods, using real-life business and financial data, while introducing d=
elegates=20
to a variety of modern Econometric Packages. Several software packages wi=
ll be=20
used throughout the course, including among others PcGive Professional, S=
tamp=20
and RATS.

Who is the course for?
People who have studied economics and finance to a good level but increas=
ingly=20
find that their skills are being overtaken by modern developments in the =
field.=20
 Our four-day course, a synthesis of similar courses taught at Cambridge =
and=20
Oxford Universities, is designed to meet at least the following four obje=
ctives:
=B7 Increase attendees' familiarity with recent developments in financial=
 economics=20
and econometric practice;
=B7 Encourage modelling of a variety of models: noise traders; bubbles; n=
on-linearities;=20
time-varying risk; cointegration methods; rational expectations and heter=
oscedasticity;
=B7 Provide real-world and worked examples for attendees to use;
=B7 Introduce users to several modern econometric packages.


The Principal Lecturers - The principal lecturers are:
Jagjit S. Chadha.  Currently Fellow in Economics at Clare College, Univer=
sity=20
of Cambridge.  Previously holding teaching and research positions at the =
University=20
of Southampton, the London School of Economics, and the Monetary Analysis=
 Division=20
of the Bank of England, in addition to various research and consulting po=
sitions=20
in financial companies of the City.

Lucio Sarno.  Currently Fellow in Economics at University College, Univer=
sity=20
of Oxford; Research Affiliate, Centre for Economic Policy Research, Londo=
n; Consultant=20
to the Research Department, Federal Reserve Bank of St. Louis, USA.  Prev=
iously=20
holding teaching and research positions at Columbia University, Brunel Un=
iversity,=20
and the University of Liverpool, in addition to research and consulting p=
ositions=20
at the World Bank and the European Commission.

Further details: www.timberlake.co.uk

5. Gauss version 3.5
There are good news for those awaiting version 3.5 of Gauss. It can be do=
wnloaded=20
from Aptech's Web site. The instructions are below:

Access Aptech's FTP site and download Gauss for Windows 3.5 free of charg=
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FTP instructions:

ftp site: 199.29.185.98

u s e r n a m e: winship

p a s s w o r d: abx47qkz

If you are using a browser to ftp to this site you must supply a username=
 in=20
the ftp command line:

ftp://u s e r n a m e:p a s s w o r d@199.29.185.98

Once logged on, you will be placed in your home directory and will have a=
ccess=20
to all file contained in that subdirectory and no others. Remember to set=
 the=20
transfer protocol to "bin" before downloading binary files. Use the "get"=
 command=20
to get the files you want off the ftp site.  You will get 120 days FREE T=
ech=20
Support. If you want continuing support, please request our Sales Departm=
ent=20
for pricing information.

Alternatively, you may prefer to receive a CD Rom (only available around =
mid=20
July). If so, request it at Gauss35@timberlake.co.uk. Please send us your=
 Gauss=20
serial number and full address details.

Please note that this release of Gauss for Windows does contain a license=
 manager=20
and at a certain stage you will need to contact us with the following inf=
ormation.=20
You can fax, email or post this form back to us.

For orders or further details in any of our services contact:

Head Office: info@timberlake.co.uk
U.S.A Office: info@timberlake-consultancy.com
Italian Office: timberlake@arc.it
Portuguese Office: timberlake.co@mail.telepac.pt
Spanish Office: timberlake@zoom.es

I look forward to hearing from you,

Ana Timberlake,				tel: +44 (0)20 86973377
Timberlake Consultants Ltd., 		fax:+44 (0)20 86973388
Unit B3, Broomsleigh Business Park,		e-mail: info@timberlake.co.uk
Worsley Bridge Road,			http://www.timberlake.co.uk
London SE26 5BN, 			http://www.timberlake-consultancy.com
U.K.

The information we will be sending you is relevant to all statisticians a=
nd econometricians.=20
However, if you do not want to continue receiving our e-mails, please ret=
urn=20
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---------- End of message ----------

From: Rob Trevor <robt@mafc.mq.edu.au>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Newsflash: Special Offers on Training
Date: Sat, 10 Jun 2000 09:54:51 +1000
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Sender: Maiser@efs01.efs.mq.edu.au
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X-Mailer: Mercury MTS (Bindery) v1.40

Ana (and anybody else who may be tempted to do the same thing)

Please do not use this list to advertise commercial products, 
especially when it is only peripherally related to RATS. Otherwise I 
will be forced to block your whole domain from this list.

This is meant to be a high signal to noise ratio list for 
discussing/helping each other with the RATS econometric software. We 
have over 500 subscribers. If you want to keep those people as part 
of this list, then please keep your postings "pure".

I'm sure that your posting was an oversight. Please do not let it happen again.

Thank you for your understanding

Rob Trevor
RATS-L Administrator

---------- End of message ----------

From: Ricardo Chaves Lima <rcl@netpe.com.br>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Help on Seazonal Unit Root test
Date: Thu, 08 Jun 2000 00:30:59 -0300
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
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Please

Daoes anyone knows any RATS  procedure for seazonal unit roots
test. Thanks a lot.

Ricardo Chaves Lima
rcl@netpe.com.br
rlima@npd.ufpe.br


---------- End of message ----------

From: Yuen Phui Ling Hazel <fbap8383@nus.edu.sg>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: RE: DISPLAY OF RESIDUALS CORRELATION
Date: Sat, 10 Jun 2000 13:08:32 +0800
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
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Content-Type: text/plain;
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HI Andreas!=20

Thanks for your kind reply once again!!
Hazel=20

 -----Original Message-----
From: 	Andreas Faust [mailto:andreasfaust@yahoo.com]=20
Sent:	Friday, June 09, 2000 8:30 PM
To:	RATS Discussion List
Subject:	Re: DISPLAY OF RESIDUALS CORRELATION

Hi Hazel,
if you will use finally the VAR.SRC you have the
possibility to see the correlation/error after
estimation. Also you can display the ACF of the
residuals. Try it!

Andreas


--- Yuen Phui Ling Hazel <fbap8383@nus.edu.sg>
schrieb: >=20
> 		Hi everyone,
>=20
> 		Does someone know how to display the correlations
> of
> residuals/ errors of a VAR system?=20
>=20
> 		Thanks very much.=20
>=20
> 		Have a Nice day.=20
> 		Hazel =20
>=20
> 		=20
> 				 -----Original Message-----
> 				From: 	Yuen Phui Ling Hazel =20
> 				Sent:	Tuesday, May 02, 2000 7:37 PM
> 				To:	'RATS-L@EFS.MQ.EDU.AU'
> 				Subject:	VMA Syntax
> 				Importance:	High
>=20
> 				Does anyone know the VMA syntax and
> procedure in RATS, apart from the one posted on the
> web?
>=20
>=20
> 				Hazel 	   fbap8383@nus.edu.sg
> 				University of Singapore=20


=3D=3D=3D=3D=3D
Andreas Faust
Av. Car=FApano N=B0 23
Qta. El Rosedal
Las Palmas, Caracas
Venezuela
Tel.: +58  2 7818621
andreasfaust@yahoo.com

__________________________________________________
Do You Yahoo!?
Yahoo! Photos -- now, 100 FREE prints!
http://photos.yahoo.com

---------- End of message ----------

From: Carlos Quintanilla <carlosq@umich.edu>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Help on Seazonal Unit Root test
Date: Sat, 10 Jun 2000 12:54:36 -0400
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
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Ricardo:
You can find a procedure at the Estima Web Page:
http://www.estima.com/procindx.htm

The name of the file is HEGY.SRC

\Carlos

At 12:30 AM 6/8/00 -0300, you wrote:
>Please
>
>Daoes anyone knows any RATS  procedure for seazonal unit roots
>test. Thanks a lot.
>
>Ricardo Chaves Lima
>rcl@netpe.com.br
>rlima@npd.ufpe.br


-------------------------------------------------------------------------
Carlos Quintanilla
University of Michigan
phone : (313) 747 7956
e-mail: carlosq@umich.edu
-------------------------------------------------------------------------


---------- End of message ----------

From: Ricardo Chaves Lima <rcl@netpe.com.br>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Help on Seazonal Unit Root test
Date: Thu, 08 Jun 2000 23:31:05 -0300
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
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Thanks Carlos




Carlos Quintanilla wrote:

> Ricardo:
> You can find a procedure at the Estima Web Page:
> http://www.estima.com/procindx.htm
>
> The name of the file is HEGY.SRC
>
> \Carlos
>
> At 12:30 AM 6/8/00 -0300, you wrote:
> >Please
> >
> >Daoes anyone knows any RATS  procedure for seazonal unit roots
> >test. Thanks a lot.
> >
> >Ricardo Chaves Lima
> >rcl@netpe.com.br
> >rlima@npd.ufpe.br
>
> -------------------------------------------------------------------------
> Carlos Quintanilla
> University of Michigan
> phone : (313) 747 7956
> e-mail: carlosq@umich.edu
> -------------------------------------------------------------------------


---------- End of message ----------

From: "Timberlake Consultants Ltd" <info@timberlake.co.uk>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Newsflash: Special Offers on Training
Date: Mon, 12 Jun 2000 07:52:37 +0100
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
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I am sorry. The mailing wans not intended to be sent to the a whole mailing.
I will remove the address from our database.

LOOK IN http://www.timberlake.co.uk/ FOR DETAILS ON OUR INTERNET AND PUBLIC
ATTENDANCE COURSES
Regards

Ana Timberlake
For and on behalf of Timberlake Consultants Ltd
Unit B3, Broomsleigh Business Park, Worsley Bridge Road, London SE26 5BN,
United Kingdom
Tel: +44 (0)208 6973377, Fax: +44 (0)208 6973388
e-mail: ana@timberlake.co.uk
URL: http://www.timberlake.co.uk/
----- Original Message -----
From: Rob Trevor <robt@mafc.mq.edu.au>
To: RATS Discussion List <RATS-L@efs.mq.edu.au>
Sent: 10 June 2000 00:54
Subject: Re: Newsflash: Special Offers on Training


> Ana (and anybody else who may be tempted to do the same thing)
>
> Please do not use this list to advertise commercial products,
> especially when it is only peripherally related to RATS. Otherwise I
> will be forced to block your whole domain from this list.
>
> This is meant to be a high signal to noise ratio list for
> discussing/helping each other with the RATS econometric software. We
> have over 500 subscribers. If you want to keep those people as part
> of this list, then please keep your postings "pure".
>
> I'm sure that your posting was an oversight. Please do not let it happen
again.
>
> Thank you for your understanding
>
> Rob Trevor
> RATS-L Administrator
>


---------- End of message ----------

From: David Teall <david_teall@yahoo.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: GED and Student-t distribution
Date: Mon, 12 Jun 2000 09:06:43 -0700 (PDT)
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
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Dear RATS users:

I am a new RATS user and wonder if anyone knows how to
write RATS codes for the log-likelihood functions of
generalized error distribution (GED) and Student-t
distribution in matrix forms (i.e., more than one
variable).  Thank you very much for your help.

Sincerely,

David

__________________________________________________
Do You Yahoo!?
Yahoo! Photos -- now, 100 FREE prints!
http://photos.yahoo.com

---------- End of message ----------

From: =?iso-8859-1?q?slim=20skandes?= <slim_skander@yahoo.fr>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: request for  a program
Date: Tue, 13 Jun 2000 17:30:50 +0200 (CEST)
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
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Hello=20

I m a student in PARIS X university (France).I m
preparing a working paper dealing with the presence of
long memory in finantial markets.

can you send me the program (for RATS ) computing the
hurst exponent with the modified rescaled range method
or tell me where can i find it.

thank you



___________________________________________________________
Do You Yahoo!?
Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr

---------- End of message ----------

From: "Stephan Kohns" <kohns@iiw.uni-bonn.de>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: choice of functional form in NLLS-estimation
Date: Tue, 13 Jun 2000 17:39:32 +0200
Errors-to: <rats-l-owner@efs.mq.edu.au>
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Dear RATS users,
 I am estimating a nonlinear Euler equation with GMM, using the method
recommended in the manual on page 5-23 (i.e. NLLS in two steps with an
adjusted weighting-matrix computed by MCOV for the second step). There are
two alternative versions for the Euler equation: The first looks like
gam*L(t)+lam*Z(t)+..., where gam and lam are two of the parameters to be
estimated and L(t) and Z(t) variables. In the second version, the whole
equation has been divided by gam, so that it looks like
L(t)+(lam/gam)*Z(t)+... .
I intend to extend the analysis to a multivariate version, so that I would
prefer the first version which is "less nonlinear" and should therefore be
computationally less demanding. Unfortunately, the estimates of the
parameters differ between the two versions, most of them by an order of
about 20%, even though I expected them to be roughly identical. I
experimented with the starting values and the convergence criterion, but the
phenomenon did not disappear.
 Can somebody give me a clue how to solve this problem? Maybe that my logic
is flawed, i.e. the estimates should be different, but in this case I am
wondering which is the specification I should use when defining my FRML.

 Thank you very much for your help,
 Stephan Kohns



---------- End of message ----------

From: "Christopher F. Baum" <baum@bc.edu>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: request for  a program
Date: Tue, 13 Jun 2000 12:08:49 -0400
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Sender: Maiser@efs01.efs.mq.edu.au
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I suggest you consider use of the GPH (Geweke/Porter-Hudak) estimation 
technique (code for which is available at Estima's web site). I also have 
RATS code for some of P.M. Robinson's semiparametric routines. Either would =

be an improvement over R/S.

Kit Baum
Boston College Economics

--On Tuesday, June 13, 2000 17:30 +0200 slim skandes 
<slim_skander@yahoo.fr> wrote:

> Hello
>
> I m a student in PARIS X university (France).I m
> preparing a working paper dealing with the presence of
> long memory in finantial markets.
>
> can you send me the program (for RATS ) computing the
> hurst exponent with the modified rescaled range method
> or tell me where can i find it.
>
> thank you
>
>
>
> ___________________________________________________________
> Do You Yahoo!?
> Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr



-----------------------------------------------------------------
Kit Baum    baum@bc.edu    http://fmwww.bc.edu/ec-v/baum.fac.html

---------- End of message ----------

From: Choyleva Diana <Diana.Choyleva@lombard-st.co.uk>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: 
Date: Wed, 14 Jun 2000 12:13:02 +0100
Errors-to: <rats-l-owner@efs.mq.edu.au>
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Hallo,

I would appreciate it if someone could help me with a problem I incurred. I
was using a program in Rats to estimate potential output using the
structural approach and then smoothing with an HPfilter. I find that when I
use different lambdas in the HPfilter i tend to get the same potential
output growth rates for the last four years and different ones for the rest.
It seems strange to me. I was wondering whether this is a feature of the
HPfilter or there must be something wrong with the program.
Thank you!

diana.choyleva@lombard-st.co.uk
 
Lombard Street Research's material is intended to encourage better
understanding of economic policy and financial markets. It does not
constitute a solicitation for the purchase or sale of any commodities,
securities or investments. Although the information compiled herein is
considered reliable, its accuracy is not guaranteed. Any person using
Lombard Street Research's material does so solely at his own risk and
Lombard Street Research shall be under no liability whatsoever in
respect thereof.



---------- End of message ----------

From: "Torben Mark Pedersen" <TMP@OEM.DK>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: HP-filter
Date: Wed, 14 Jun 2000 13:53:25 +0200
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Sender: Maiser@efs01.efs.mq.edu.au
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Dear Diana Choyleva

1. From your description of the problem, it does seem like there is =
something wrong. The deviation of output from trend should depend =
critically on the value of the smoothing parameter, lambda, in the =
HP-filter, though you should be aware of the fact that it takes large =
changes in the value of lambda to get quantitatively large differences.=20

2. The HP-filter works like a symmetric, infinite time horizon weighted =
moving average filter in the time domain, so there are some serious =
end-point problems with the HP-filter. Near the end of the sample, the =
HP-filter works like a one-sided filter and is consequently distorting =
near the ends of the sample.  Noone seems to have analyzed the endpoint =
problems in the time domain in a quantitative way, but it can be seriously =
misleading to use the deviation of output from the HP-trend as a measure =
of potential output. That measure may be seriously distorted by the =
endpoint problems.=20


Sincerely,


Torben Mark Pedersen
Ministry of Economic Affairs
Ved Stranden
DK-1061 Copenhagen K.
Denmark

E-mail: tmp@oem.dk




>>> Diana.Choyleva@lombard-st.co.uk 14-06-00 13:13 >>>
Hallo,

I would appreciate it if someone could help me with a problem I incurred. =
I
was using a program in Rats to estimate potential output using the
structural approach and then smoothing with an HPfilter. I find that when =
I
use different lambdas in the HPfilter i tend to get the same potential
output growth rates for the last four years and different ones for the =
rest.
It seems strange to me. I was wondering whether this is a feature of the
HPfilter or there must be something wrong with the program.
Thank you!

diana.choyleva@lombard-st.co.uk=20
=20
Lombard Street Research's material is intended to encourage better
understanding of economic policy and financial markets. It does not
constitute a solicitation for the purchase or sale of any commodities,
securities or investments. Although the information compiled herein is
considered reliable, its accuracy is not guaranteed. Any person using
Lombard Street Research's material does so solely at his own risk and
Lombard Street Research shall be under no liability whatsoever in
respect thereof.




---------- End of message ----------

From: Simon van Norden <Simon.van-Norden@hec.ca>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: HP-filter
Date: Wed, 14 Jun 2000 09:11:34 -0400
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Sender: Maiser@efs01.efs.mq.edu.au
X-listname: <RATS-L@efs01.efs.mq.edu.au>
Organization: Ecole des Hautes Etudes Commerciales
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Actually, we recently did a quantitative study of the end point problems =
with
the HP filter and several other popular univariate detrending methods in =
the
context of measuring potential output. Our results confirm what Dr. Peder=
sen
wrote. We also have several references to other papers on this and relate=
d
issues.

The paper is "The Reliability of Output Gap Estimates in Real Time" by
Orphanides and van Norden. You can find it as FEDS working paper 1999-38,
available on my homepage (see below) or from the Federal Reserve Board.

Regards,

SvN

Torben Mark Pedersen wrote:
>=20
> Dear Diana Choyleva
>=20
> 1. From your description of the problem, it does seem like there is som=
ething wrong. The deviation of output from trend should depend critically=
 on the value of the smoothing parameter, lambda, in the HP-filter, thoug=
h you should be aware of the fact that it takes large changes in the valu=
e of lambda to get quantitatively large differences.
>=20
> 2. The HP-filter works like a symmetric, infinite time horizon weighted=
 moving average filter in the time domain, so there are some serious end-=
point problems with the HP-filter. Near the end of the sample, the HP-fil=
ter works like a one-sided filter and is consequently distorting near the=
 ends of the sample.  Noone seems to have analyzed the endpoint problems =
in the time domain in a quantitative way, but it can be seriously mislead=
ing to use the deviation of output from the HP-trend as a measure of pote=
ntial output. That measure may be seriously distorted by the endpoint pro=
blems.
>=20
> Sincerely,
>=20
> Torben Mark Pedersen
> Ministry of Economic Affairs
> Ved Stranden
> DK-1061 Copenhagen K.
> Denmark
>=20
> E-mail: tmp@oem.dk
>=20
> >>> Diana.Choyleva@lombard-st.co.uk 14-06-00 13:13 >>>
> Hallo,
>=20
> I would appreciate it if someone could help me with a problem I incurre=
d. I
> was using a program in Rats to estimate potential output using the
> structural approach and then smoothing with an HPfilter. I find that wh=
en I
> use different lambdas in the HPfilter i tend to get the same potential
> output growth rates for the last four years and different ones for the =
rest.
> It seems strange to me. I was wondering whether this is a feature of th=
e
> HPfilter or there must be something wrong with the program.
> Thank you!
>=20
> diana.choyleva@lombard-st.co.uk
>=20
> Lombard Street Research's material is intended to encourage better
> understanding of economic policy and financial markets. It does not
> constitute a solicitation for the purchase or sale of any commodities,
> securities or investments. Although the information compiled herein is
> considered reliable, its accuracy is not guaranteed. Any person using
> Lombard Street Research's material does so solely at his own risk and
> Lombard Street Research shall be under no liability whatsoever in
> respect thereof.

--=20
Simon van Norden, Prof. agr=E9g=E9, www.hec.ca/pages/simon.van-norden
Service de l'enseignement de la finance, =C9cole des H.E.C.
3000 Cote-Sainte-Catherine, Montreal QC, CANADA   H3T 2A7
simon.van-norden@hec.ca or (514)340-6781 or fax:(514)340-5632

---------- End of message ----------

From: =?iso-8859-1?q?slim=20skandes?= <slim_skander@yahoo.fr>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: request for  a program
Date: Wed, 14 Jun 2000 16:47:51 +0200 (CEST)
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Sender: Maiser@efs01.efs.mq.edu.au
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X-Mailer: Mercury MTS (Bindery) v1.40

Hello=20
I m a student in PARIS X university (France).I m
preparing a working paper dealing with the presence of
long memory in finantial markets.
I have programs computing the hurst exponent by the
rescaled range method and the GPH method (Geweke
Porter-Hudak). I want to apply the modified rescaled
range method proposed by A.Lo (1991).
AS i m beggining with RATS i couldn't do the progam .
can you send me the program (for RATS ) computing the
hurst exponent with the modified rescaled range
methodor tell me where can i find them.
please help me

thank you





___________________________________________________________
Do You Yahoo!?
Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr

---------- End of message ----------

From: "Timberlake Consultants Ltd" <info@timberlake.co.uk>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: request for  a program
Date: Wed, 14 Jun 2000 16:18:06 +0100
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Sender: Maiser@efs01.efs.mq.edu.au
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We are working on it.

Please visit our Web for details on our Internet and Public Attendance
courses

Regards
Ana Timberlake
Timberlake Consultants Limited
http://www.timberlake.co.uk
Unit B3, Broomsleigh Business Park,
Worsley Bridge Road, London SE26 5BN, U.K.
Tel: +44 (0)20 86973377   Fax: +44 (0)20 86973388  e-mail:
ana@timberlake.co.uk
----- Original Message -----
From: slim skandes <slim_skander@yahoo.fr>
To: RATS Discussion List <RATS-L@efs.mq.edu.au>
Sent: 14 June 2000 15:47
Subject: request for a program


> Hello
> I m a student in PARIS X university (France).I m
> preparing a working paper dealing with the presence of
> long memory in finantial markets.
> I have programs computing the hurst exponent by the
> rescaled range method and the GPH method (Geweke
> Porter-Hudak). I want to apply the modified rescaled
> range method proposed by A.Lo (1991).
> AS i m beggining with RATS i couldn't do the progam .
> can you send me the program (for RATS ) computing the
> hurst exponent with the modified rescaled range
> methodor tell me where can i find them.
> please help me
>
> thank you
>
>
>
>
>
> ___________________________________________________________
> Do You Yahoo!?
> Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr
>


---------- End of message ----------

From: Klaus Fischer <Klaus.Fischer@fas.ulaval.ca>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Timberlake Consultants
Date: Wed, 14 Jun 2000 12:52:36 -0400
Errors-to: <rats-l-owner@efs.mq.edu.au>
Reply-to: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Sender: Maiser@efs01.efs.mq.edu.au
X-listname: <RATS-L@efs01.efs.mq.edu.au>
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MIME-Version: 1.0
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Dear Ana:

I don not know what the the answer is to Slim's question about long memor=
y
in financial markets, but I am sure that there are probably better answer=
s
than to sending him/her to take a course with your consulting group.
What's next, the price list for your courses? I think you should try to
stop exploiting this list for your business purposes. We got the message
that you exist. If you do not have a direct answer to a direct question
leave us alone.

And I suspect I am being kind in the way I said it.

Yours,

Klaus Fischer

Timberlake Consultants Ltd wrote:

> We are working on it.
>
> Please visit our Web for details on our Internet and Public Attendance
> courses
>
> Regards
> Ana Timberlake
> Timberlake Consultants Limited
> http://www.timberlake.co.uk
> Unit B3, Broomsleigh Business Park,
> Worsley Bridge Road, London SE26 5BN, U.K.
> Tel: +44 (0)20 86973377   Fax: +44 (0)20 86973388  e-mail:
> ana@timberlake.co.uk
> ----- Original Message -----
> From: slim skandes <slim_skander@yahoo.fr>
> To: RATS Discussion List <RATS-L@efs.mq.edu.au>
> Sent: 14 June 2000 15:47
> Subject: request for a program
>
> > Hello
> > I m a student in PARIS X university (France).I m
> > preparing a working paper dealing with the presence of
> > long memory in finantial markets.
> > I have programs computing the hurst exponent by the
> > rescaled range method and the GPH method (Geweke
> > Porter-Hudak). I want to apply the modified rescaled
> > range method proposed by A.Lo (1991).
> > AS i m beggining with RATS i couldn't do the progam .
> > can you send me the program (for RATS ) computing the
> > hurst exponent with the modified rescaled range
> > methodor tell me where can i find them.
> > please help me
> >
> > thank you
> >
> >
> >
> >
> >
> > ___________________________________________________________
> > Do You Yahoo!?
> > Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr
> >


---------- End of message ----------

From: SsnaithIPR@aol.com
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Timberlake Consultants
Date: Wed, 14 Jun 2000 15:17:43 EDT
Errors-to: <rats-l-owner@efs.mq.edu.au>
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In a message dated 6/14/2000 1:10:59 PM Eastern Daylight Time, 
Klaus.Fischer@fas.ulaval.ca writes:

I think it may be time to block e-mails from this domain.   Rob warned her 
politely but very clearly and her she is again pitching her site?  What's 
next on the list adult web sites?

Further if this person is so slow on the uptake, one wonders about the 
quality of the services being offered...

This list is a valuable resource let's not let someone like this ruin it.

> Dear Ana:
>  
>  I don not know what the the answer is to Slim's question about long memory
>  in financial markets, but I am sure that there are probably better answers
>  than to sending him/her to take a course with your consulting group.
>  What's next, the price list for your courses? I think you should try to
>  stop exploiting this list for your business purposes. We got the message
>  that you exist. If you do not have a direct answer to a direct question
>  leave us alone.
>  
>  And I suspect I am being kind in the way I said it.
>  
>  Yours,
>  
>  Klaus Fischer
>  

---------- End of message ----------

From: Jason Morris <jasonwm@email.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Timberlake Consultants
Date: Wed, 14 Jun 2000 16:08:44 -0400 (EDT)
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Hi!

I'm curious.  Is this Dr Snaith who Lectured Econometrics at UWI Jamaica,
last year?

If not, I'm sorry to bother you.

Jason

-----------------------------------------------
FREE! The World's Best Email Address @email.com
Reserve your name now at http://www.email.com



---------- End of message ----------

From: =?iso-8859-1?q?slim=20skandes?= <slim_skander@yahoo.fr>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: request for  a program
Date: Thu, 15 Jun 2000 13:11:25 +0200 (CEST)
Errors-to: <rats-l-owner@efs.mq.edu.au>
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Hello=20
I m a student in PARIS X university (France).I m
preparing a working paper dealing with the presence of
long memory in finantial markets.
I have programs computing the hurst exponent by the
rescaled range method and the GPH method (Geweke
Porter-Hudak). I want to apply the modified rescaled
range method proposed by A.Lo (1991).
AS i m beggining with RATS i couldn't do the progam .
can you send me the program (for RATS ) computing the
hurst exponent with the modified rescaled range
methodor tell me where can i find them.
please help me

thank you





___________________________________________________________
Do You Yahoo!?
Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr

---------- End of message ----------

From: "Crowley, Patrick" <pcrowley@jaguar.middlebury.edu>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: RE: HP-filter
Date: Thu, 15 Jun 2000 12:00:02 -0400
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Dear Rats users,

While we're on with the HP filter, I'm trying to use the HP filter on =
annual
data for Canadian provinces, as that's all there is available, and =
there
aren't many datapoints - 26 to be exact.  How many datapoints do you =
think
are necessary to run an HP filter, and what value of lambda would you =
advise
for annual data?

Patrick Crowley
Dept of Economics,
Middlebury College.
 =20

-----Original Message-----
From: Simon van Norden
To: RATS Discussion List
Sent: 6/14/00 9:11 AM
Subject: Re: HP-filter

Actually, we recently did a quantitative study of the end point =
problems
with
the HP filter and several other popular univariate detrending methods =
in
the
context of measuring potential output. Our results confirm what Dr.
Pedersen
wrote. We also have several references to other papers on this and
related
issues.

The paper is "The Reliability of Output Gap Estimates in Real Time" by
Orphanides and van Norden. You can find it as FEDS working paper
1999-38,
available on my homepage (see below) or from the Federal Reserve Board.

Regards,

SvN

Torben Mark Pedersen wrote:
>=20
> Dear Diana Choyleva
>=20
> 1. From your description of the problem, it does seem like there is
something wrong. The deviation of output from trend should depend
critically on the value of the smoothing parameter, lambda, in the
HP-filter, though you should be aware of the fact that it takes large
changes in the value of lambda to get quantitatively large differences.
>=20
> 2. The HP-filter works like a symmetric, infinite time horizon
weighted moving average filter in the time domain, so there are some
serious end-point problems with the HP-filter. Near the end of the
sample, the HP-filter works like a one-sided filter and is consequently
distorting near the ends of the sample.  Noone seems to have analyzed
the endpoint problems in the time domain in a quantitative way, but it
can be seriously misleading to use the deviation of output from the
HP-trend as a measure of potential output. That measure may be =
seriously
distorted by the endpoint problems.
>=20
> Sincerely,
>=20
> Torben Mark Pedersen
> Ministry of Economic Affairs
> Ved Stranden
> DK-1061 Copenhagen K.
> Denmark
>=20
> E-mail: tmp@oem.dk
>=20
> >>> Diana.Choyleva@lombard-st.co.uk 14-06-00 13:13 >>>
> Hallo,
>=20
> I would appreciate it if someone could help me with a problem I
incurred. I
> was using a program in Rats to estimate potential output using the
> structural approach and then smoothing with an HPfilter. I find that
when I
> use different lambdas in the HPfilter i tend to get the same =
potential
> output growth rates for the last four years and different ones for =
the
rest.
> It seems strange to me. I was wondering whether this is a feature of
the
> HPfilter or there must be something wrong with the program.
> Thank you!
>=20
> diana.choyleva@lombard-st.co.uk
>=20
> Lombard Street Research's material is intended to encourage better
> understanding of economic policy and financial markets. It does not
> constitute a solicitation for the purchase or sale of any =
commodities,
> securities or investments. Although the information compiled herein =
is
> considered reliable, its accuracy is not guaranteed. Any person using
> Lombard Street Research's material does so solely at his own risk and
> Lombard Street Research shall be under no liability whatsoever in
> respect thereof.

--=20
Simon van Norden, Prof. agr=E9g=E9, www.hec.ca/pages/simon.van-norden
Service de l'enseignement de la finance, =C9cole des H.E.C.
3000 Cote-Sainte-Catherine, Montreal QC, CANADA   H3T 2A7
simon.van-norden@hec.ca or (514)340-6781 or fax:(514)340-5632

---------- End of message ----------

From: Simon van Norden <Simon.van-Norden@hec.ca>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: HP-filter
Date: Thu, 15 Jun 2000 13:49:55 -0400
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Pat;

It's hard to give a precise answer, since it's not clear why and how the =
HP
filter is being used.

Hodrick & Prescott argued that their filter gave "reasonable-looking resu=
lts."
On that basis, you should choose any lambda that gives "reasonable-lookin=
g
results."
This will probably be 100 or less. (You can also formally define a state-=
space
model whose optimal smoother is the HP filter and then estimate the optim=
al
lambda by maximum-likelihood methods. However, this is rarely done and do=
esn't
give anything close to 1600 on quarterly data.)

As for the number of data points, the same problem applies. Technically, =
I think
you only need 3 or 4. Realistically, I assume you're worried about endpoi=
nt
problems. The severity of this problem will depend on the lambda you choo=
se, so
it's hard to give a simple rule. I'd suggest that you look at the MA
representation of the filter weights and make sure they are still fairly
symmetric around the points you choose to include.

A simple alternative might be to use the BPFILTER.SRC proc from Estima to=
 do
band-pass filtering instead.=20

Another would be to detrend linearly, using recursive breakpoint tests to=
 allow
for changes in the slope of the trend.


Simon

"Crowley, Patrick" wrote:
>=20
> Dear Rats users,
>=20
> While we're on with the HP filter, I'm trying to use the HP filter on a=
nnual
> data for Canadian provinces, as that's all there is available, and ther=
e
> aren't many datapoints - 26 to be exact.  How many datapoints do you th=
ink
> are necessary to run an HP filter, and what value of lambda would you a=
dvise
> for annual data?
>=20
> Patrick Crowley
> Dept of Economics,
> Middlebury College.
>=20
>=20
> -----Original Message-----
> From: Simon van Norden
> To: RATS Discussion List
> Sent: 6/14/00 9:11 AM
> Subject: Re: HP-filter
>=20
> Actually, we recently did a quantitative study of the end point problem=
s
> with
> the HP filter and several other popular univariate detrending methods i=
n
> the
> context of measuring potential output. Our results confirm what Dr.
> Pedersen
> wrote. We also have several references to other papers on this and
> related
> issues.
>=20
> The paper is "The Reliability of Output Gap Estimates in Real Time" by
> Orphanides and van Norden. You can find it as FEDS working paper
> 1999-38,
> available on my homepage (see below) or from the Federal Reserve Board.
>=20
> Regards,
>=20
> SvN
>=20
> Torben Mark Pedersen wrote:
> >
> > Dear Diana Choyleva
> >
> > 1. From your description of the problem, it does seem like there is
> something wrong. The deviation of output from trend should depend
> critically on the value of the smoothing parameter, lambda, in the
> HP-filter, though you should be aware of the fact that it takes large
> changes in the value of lambda to get quantitatively large differences.
> >
> > 2. The HP-filter works like a symmetric, infinite time horizon
> weighted moving average filter in the time domain, so there are some
> serious end-point problems with the HP-filter. Near the end of the
> sample, the HP-filter works like a one-sided filter and is consequently
> distorting near the ends of the sample.  Noone seems to have analyzed
> the endpoint problems in the time domain in a quantitative way, but it
> can be seriously misleading to use the deviation of output from the
> HP-trend as a measure of potential output. That measure may be seriousl=
y
> distorted by the endpoint problems.
> >
> > Sincerely,
> >
> > Torben Mark Pedersen
> > Ministry of Economic Affairs
> > Ved Stranden
> > DK-1061 Copenhagen K.
> > Denmark
> >
> > E-mail: tmp@oem.dk
> >
> > >>> Diana.Choyleva@lombard-st.co.uk 14-06-00 13:13 >>>
> > Hallo,
> >
> > I would appreciate it if someone could help me with a problem I
> incurred. I
> > was using a program in Rats to estimate potential output using the
> > structural approach and then smoothing with an HPfilter. I find that
> when I
> > use different lambdas in the HPfilter i tend to get the same potentia=
l
> > output growth rates for the last four years and different ones for th=
e
> rest.
> > It seems strange to me. I was wondering whether this is a feature of
> the
> > HPfilter or there must be something wrong with the program.
> > Thank you!
> >
> > diana.choyleva@lombard-st.co.uk
> >
> > Lombard Street Research's material is intended to encourage better
> > understanding of economic policy and financial markets. It does not
> > constitute a solicitation for the purchase or sale of any commodities=
,
> > securities or investments. Although the information compiled herein i=
s
> > considered reliable, its accuracy is not guaranteed. Any person using
> > Lombard Street Research's material does so solely at his own risk and
> > Lombard Street Research shall be under no liability whatsoever in
> > respect thereof.
>=20
> --
> Simon van Norden, Prof. agr=E9g=E9, www.hec.ca/pages/simon.van-norden
> Service de l'enseignement de la finance, =C9cole des H.E.C.
> 3000 Cote-Sainte-Catherine, Montreal QC, CANADA   H3T 2A7
> simon.van-norden@hec.ca or (514)340-6781 or fax:(514)340-5632

--=20
Simon van Norden, Prof. agr=E9g=E9, www.hec.ca/pages/simon.van-norden
Service de l'enseignement de la finance, =C9cole des H.E.C.
3000 Cote-Sainte-Catherine, Montreal QC, CANADA   H3T 2A7
simon.van-norden@hec.ca or (514)340-6781 or fax:(514)340-5632

---------- End of message ----------

From: Hermanto Siregar <siregah@kea.lincoln.ac.nz>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: RE: HP-filter
Date: Fri, 16 Jun 2000 09:21:10 +1200
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On Thu, 15 Jun 2000 12:00 "Crowley, Patrick" wrote:
> are necessary to run an HP filter, and what value of lambda would you advise
> for annual data?

Dear Patrick,
Harvey and Jaeger (1993) demonstrate that for lambda=1600 the 
transfer function for the HP filter peaks around 30.1 quarters (about 
7.5 years), suggesting to use lambda=7 for annual data. In general 
however the optimal choice of lambda depends on particular series.
Regards,


Hermanto Siregar

---------- End of message ----------

From: anjun zhou <a-zhou@students.uiuc.edu>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Unsubscribe
Date: Thu, 15 Jun 2000 19:49:36 -0500 (CDT)
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Please take me off the list.  Thanks.

Anjun Zhou


---------- End of message ----------

From: "Torben Mark Pedersen" <TMP@OEM.DK>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Vedr.: RE: HP-filter
Date: Fri, 16 Jun 2000 08:39:28 +0200
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Dear Patrick Crowley

In a forthcoming paper in Journal of Economic Dynamics and Control, I show =
how to compute the optimal value of lambda when filtering different time =
series depending on the definition of the cyclical component (cycles =
shorter than 8 years or shorter than 9 years etc.) and based on annual, =
quarterly, or monthly data. The optimal value of lambda is the value which =
is least distorting compared to filtering with an ideal high-pass filter.

In general, the optimal value of lambda depends on the time series being =
filtered (the spectral shape of the series).=20

For US real GDP, I find that a value of 4-5 is optimal when defining the =
cyclical component as cycles with a duration shorter than 8 years.

You can find the paper on http://www.econ.ku.dk/tmp/manuscripts.htm#Slutzky=
=20
and more details on the use with annual and monthly data on
http://www.econ.ku.dk/tmp/manuscripts.htm#Spectral

Sincerely,

Torben Mark Pedersen
Ministry of Economic Affairs
Ved Stranden 8
DK-1061 Copenhagen K.
Denmark

Tel.: +45 33924168
E-mail: tmp@oem.dk


---------- End of message ----------

From: Choyleva Diana <Diana.Choyleva@lombard-st.co.uk>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: 
Date: Fri, 16 Jun 2000 17:04:21 +0100
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Hallo,

Is a value of lambda in the HPfilter around 10000 or 4000 plausible for
quarterly data?


diana.choyleva@lombard-st.co.uk
 
Lombard Street Research's material is intended to encourage better
understanding of economic policy and financial markets. It does not
constitute a solicitation for the purchase or sale of any commodities,
securities or investments. Although the information compiled herein is
considered reliable, its accuracy is not guaranteed. Any person using
Lombard Street Research's material does so solely at his own risk and
Lombard Street Research shall be under no liability whatsoever in
respect thereof.



---------- End of message ----------

From: adolpus laidlow <alaidlow@yahoo.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Timberlake Consultants
Date: Fri, 16 Jun 2000 13:14:42 -0700 (PDT)
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--- Jason Morris <jasonwm@email.com> wrote:
> Hi!
> 
> I'm curious.  Is this Dr Snaith who Lectured
> Econometrics at UWI Jamaica,
> last year?
> 
> If not, I'm sorry to bother you.
> 
> Jason
> 


jason

i think his name is Micheal so maybe not. tell kim to
give you the grade and you'll send it because am
receiving your mails...congrats on your grade.

anyway take care

Laidlow


> -----------------------------------------------
> FREE! The World's Best Email Address @email.com
> Reserve your name now at http://www.email.com
> 
> 


__________________________________________________
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---------- End of message ----------

From: "Torben Mark Pedersen" <TMP@OEM.DK>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Vedr.:
Date: Sat, 17 Jun 2000 11:24:37 +0200
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No!

It should be around 1000-1050 for quarterly data when defining the =
cyclical component as cycles with a duration shorter than 8 years. The =
value of lambda depends on the time series being filtered.

Sincerely,

Torben Mark Pedersen
Ministry of Economic Affairs
Ved Stranden 8
DK-1061 Copenhagen K
Denmark



>>> Diana.Choyleva@lombard-st.co.uk 16-06-00 18:04 >>>
Hallo,

Is a value of lambda in the HPfilter around 10000 or 4000 plausible for
quarterly data?


diana.choyleva@lombard-st.co.uk=20
=20
Lombard Street Research's material is intended to encourage better
understanding of economic policy and financial markets. It does not
constitute a solicitation for the purchase or sale of any commodities,
securities or investments. Although the information compiled herein is
considered reliable, its accuracy is not guaranteed. Any person using
Lombard Street Research's material does so solely at his own risk and
Lombard Street Research shall be under no liability whatsoever in
respect thereof.




---------- End of message ----------

From: Choyleva Diana <Diana.Choyleva@lombard-st.co.uk>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: RE: Vedr.:
Date: Mon, 19 Jun 2000 10:05:52 +0100
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What if the cyclical duration is greater than 8-9 years ( I am filtering
total productivity)?

> -----Original Message-----
> From:	Torben Mark Pedersen [SMTP:TMP@OEM.DK]
> Sent:	Saturday, June 17, 2000 10:25 AM
> To:	RATS Discussion List
> Subject:	Vedr.:
> 
> No!
> 
> It should be around 1000-1050 for quarterly data when defining the
> cyclical component as cycles with a duration shorter than 8 years. The
> value of lambda depends on the time series being filtered.
> 
> Sincerely,
> 
> Torben Mark Pedersen
> Ministry of Economic Affairs
> Ved Stranden 8
> DK-1061 Copenhagen K
> Denmark
> 
> 
> 
> >>> Diana.Choyleva@lombard-st.co.uk 16-06-00 18:04 >>>
> Hallo,
> 
> Is a value of lambda in the HPfilter around 10000 or 4000 plausible for
> quarterly data?
> 
> 
> diana.choyleva@lombard-st.co.uk 
>  
> Lombard Street Research's material is intended to encourage better
> understanding of economic policy and financial markets. It does not
> constitute a solicitation for the purchase or sale of any commodities,
> securities or investments. Although the information compiled herein is
> considered reliable, its accuracy is not guaranteed. Any person using
> Lombard Street Research's material does so solely at his own risk and
> Lombard Street Research shall be under no liability whatsoever in
> respect thereof.
> 
> 

---------- End of message ----------

From: "Torben Mark Pedersen" <TMP@OEM.DK>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: HP-filtering
Date: Mon, 19 Jun 2000 16:04:43 +0200
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I have computed the following optimal values of the smoothing parameter of =
the HP-filter (lambda)  when filtering log of US real GDP for the period =
1947-97 for quarterly, annual, and monthly time series and for hte =
following combination of cycle length:

There is some uncertainty about the estimates since there is some =
uncertainty about the true spectral shape of the US real GDP series. I =
would personally use the lower numbers in the following ranges:

cycles      Quarterly        =20

3 years    19-22
4 years    60-68
5 years    150-160
6 years    315-335
7 years    585-610
8 years    1005-1040
9 years    1620-1665
10 years  2450-2505
12 years  5215-5315
16 years  16130-16410


cycles      Annual        =20

3 years    .09-.1
4 years    .3-.5
5 years    .7-1
6 years    1.3-1.8
7 years    2.2-3.1
8 years    3.7-4.9
9 years    5.9-7.6
10 years  9-11.2
12 years  18.9-22.2
16 years  60.9-67.6


cycles      Monthly       =20

3 years    1620-1665
4 years    5210-5310
5 years    12725-12950
6 years    25900-26400
7 years    49400-50400
8 years    82800-84800
9 years    130500-134000
10 years  201000-207750
12 years  427500-447000
16 years  1378000-1482500

The technique for computing the optimal value is found in=20
http://www.econ.ku.dk/tmp/manuscripts.htm#Slutzky=20
which will be published in the Journal of Economic Dynamics and Control =
later this year.








Torben Mark Pedersen, specialkonsulent
=D8konomiministeriet
Ved Stranden 8
1061 K=F8benhavn K.
Tlf.: 33 92 41 68
E-mail: tmp@oem.dk
URL: http://www.econ.ku.dk/tmp/default.htm

Torben Mark Pedersen
Ministry of Economic Affairs
Ved Stranden 8
DK-1061 Copenhagen K.
Denmark
Tel: +45  33 92 41 68
E-mail: tmp@oem.dk
URL: http://www.econ.ku.dk/tmp/default.htm



>>> Diana.Choyleva@lombard-st.co.uk 19-06-00 11:05 >>>
What if the cyclical duration is greater than 8-9 years ( I am filtering
total productivity)?

> -----Original Message-----
> From:	Torben Mark Pedersen [SMTP:TMP@OEM.DK]=20
> Sent:	Saturday, June 17, 2000 10:25 AM
> To:	RATS Discussion List
> Subject:	Vedr.:
>=20
> No!
>=20
> It should be around 1000-1050 for quarterly data when defining the
> cyclical component as cycles with a duration shorter than 8 years. The
> value of lambda depends on the time series being filtered.
>=20
> Sincerely,
>=20
> Torben Mark Pedersen
> Ministry of Economic Affairs
> Ved Stranden 8
> DK-1061 Copenhagen K
> Denmark
>=20
>=20
>=20
> >>> Diana.Choyleva@lombard-st.co.uk 16-06-00 18:04 >>>
> Hallo,
>=20
> Is a value of lambda in the HPfilter around 10000 or 4000 plausible for
> quarterly data?
>=20
>=20
> diana.choyleva@lombard-st.co.uk=20
> =20
> Lombard Street Research's material is intended to encourage better
> understanding of economic policy and financial markets. It does not
> constitute a solicitation for the purchase or sale of any commodities,
> securities or investments. Although the information compiled herein is
> considered reliable, its accuracy is not guaranteed. Any person using
> Lombard Street Research's material does so solely at his own risk and
> Lombard Street Research shall be under no liability whatsoever in
> respect thereof.
>=20
>=20


---------- End of message ----------

From: cipolla@sbu.ac.uk
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Inequality constraints
Date: Mon, 19 Jun 2000 16:34:58 +0000
Errors-to: <rats-l-owner@efs.mq.edu.au>
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Dear RATS users,
I am estimating a GARCH(1,1) process:
y(t)=c0 + u(t)
h(t)  = (1-c1-c2) + c1*h(t-1)+c2*u{1}**2 
where u{1}**2, is the squared residual lagged once and the 
unconditional variance is normalised to unity. From the estimation 
results I obtain that both c1 and c2 are less than unity and 
positive, but their sum exceeds unity.  Can anyone help me to impose 
the constraint c1+c2 < 1, in order to achieve stability in the 
conditional variance equation? 
Many thanks
 
Andrea Cipollini
South Bank University
Business School
Southwark Campus
103 Borough Road
London SE1 0AA

Direct Line: +44 (0)171-8157077
E-mail: cipolla@sbu.ac.uk


---------- End of message ----------

From: Brian Lucey <blucey@truxa1.tcd.ie>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: stochastic dominance
Date: Mon, 19 Jun 2000 18:14:14 +0100
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anybody with experience of stochastic dominance in rats ? 
-- 
The comments etc above are my own personal views
and should not be taken as representing the official 
views of Trinity College nor of the School of Business

Brian M Lucey
Lecturer in Finance
School of Business Studies
Trinity College
Dublin 2, Ireland
353-1-6081552 (Phone)
353-1-6799503 (Fax)

---------- End of message ----------

From: JohnVelis@intesasgr.it
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Oggetto: Inequality constraints
Date: Tue, 20 Jun 2000 10:50:38 +0200
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Ciao, Andrea:

You could run an IGARCH model (integrated-GARCH) as suggested by Engle and
Bollerslev (Econometric Reviews, 1986). in which the variance equation
looks like the following:

h(t)=alpha(epsilon(t)^2) + (1-alpha)h(t-1).

There is a nicer exposition of the IGARCH model in Bera and Higgens (J Econ
Surveys, 1993).

It isn't unusual for series which are very non-stationary to have level
shifts which give you explosive variance estimates (exchange rates which
get devalued, for example -- see Baille and Bollerslve, JBES,  1989.)

Good luck.

John Velis
Chief Economist
Intesa Asset Management, SGR
Foro Buonaparte 35
20121 Milano
ITALIA

Tel:    39-02-88102525
Fax:    39-02-88102500
email:  johnvelis@intesasgr.it



---------- End of message ----------

From: Yuen Phui Ling Hazel <fbap8383@nus.edu.sg>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Matrix Multiplication with residuals 
Date: Tue, 20 Jun 2000 17:51:55 +0800
Errors-to: <rats-l-owner@efs.mq.edu.au>
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Hi everyone, 

Does someone know the syntax or has any clue as how to do matrix
multiplication of which one matrix is the residuals series, i.e. to multiply
the rectangular matrix of the residuals series with another matrix of
compatible dimension. 
 
Thanks so much in advance. 

Have a nice day. 

Kind Rgds, 
Hazel 


---------- End of message ----------

From: Allison <tzhou@hawaii.edu>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: question about BVAR
Date: Tue, 20 Jun 2000 16:28:01 -1000
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--------------E444FCC7106BBD4BFD6B362A
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit

Hi:

    I am a user of WINRATS 4.3. Lately I have been trying to reproduce
the result of
Bayesian VAR (with Minnesota prior) through a Mixed Regression program.
I am able
to get really close resemblance in the coefficients, however, they are
not identical. In
what follows, please find my program code and output. My main questions
are:
1) Does built-in BVAR procedure first demean variables?
2) If not, how to handle deterministic variables? Is my way correct?
3) What is the reason for close, however not identical, regression
coefficients?

    I look forward to your response. Thank you very much.
Allison

A) Code for mixreg.src ( identical to the example you give on page 5-13
of manual
version 4, except that I adjust the degree of freedom from T-K to T-NDET
with NDET
being number of deterministic variables)

PROCEDURE MIXED DEPVAR NDET NBEG NEND CAPR LOWR V
TYPE  SERIES      DEPVAR
TYPE  REAL        NDET
TYPE  INTEGER     NBEG  NEND ; * Estimation Range
TYPE  RECTANGULAR CAPR       ; * R matrix: m x NREG
TYPE  VECTOR      LOWR       ; * r vector: m x 1
TYPE  SYMMETRIC   V          ; * V matrix: m x m
*
LOCAL SYMMETRIC   XXMIXED
LOCAL VECTOR      XYMIXED
LOCAL INDEX       REGSUPP    ; * Array for supplementary card
*
ENTER(VARYING) REGSUPP       ; * Bring in supplementary card
CMOMENT NBEG NEND            ; * CMOM including depvar
# REGSUPP DEPVAR
LINREG(CMOM, NOPRINT) DEPVAR
# REGSUPP
OVERLAY  %CMOM(1,1)       WITH XXMIXED(%NREG,%NREG)
OVERLAY  %CMOM(%NREG+1,1) WITH XYMIXED(%NREG)
COMPUTE ADJ=(%NOBS-%NREG)/(%NOBS-NDET)
DISPLAY ADJ
COMPUTE XXMIXED=XXMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*CAPR)
COMPUTE XYMIXED=XYMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*LOWR)
LINREG(CMOM) DEPVAR
#REGSUPP
END



B) Program code for doing mixed estimation regression.

source(noecho) I:\winrats\uhero\mixreg.src
cal 60 1 4
allocate 85:4
open data I:\winrats\usadata.rat
data(format=rats) /

* Using built-in procedure to do BVAR regression with Minnesota priors
COMPUTE GAMMA=0.2
COMPUTE FIJ=0.5
system 1 to 2
variables usaprice usargnp
lags 1 to 2
det constant
specify(type=symmetric,tight=GAMMA)  FIJ
end(system)
estimate

* Mixed regression by hand

* Compute S1, the standard error of auto regression on equation 1
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USAPRICE
LINREG(CMOMENT) USAPRICE
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}

* Two alternative ways to calculate S1, one with Degree of Freedom T-K,
the other T-NDET
COMPUTE S1=SQRT(%SEESQ)
*COMPUTE TEST1=%RSS/(%NOBS-1)
*COMPUTE S1=SQRT(TEST1)
DISPLAY S1 %SEESQ

* Compute S2, the standard error of auto regression on equation 2
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USARGNP
LINREG(CMOMENT) USARGNP
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}
COMPUTE S2=SQRT(%SEESQ)
*COMPUTE TEST2=%RSS/(%NOBS-1)
*COMPUTE S2=SQRT(TEST2)
DISPLAY S2 %SEESQ

* Compute the prior information for mixed regression

COMPUTE [RECTANGULAR] R =
||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||

COMPUTE [VECTOR] LITTLER = ||1,0,0,0,0||
COMPUTE [SYMMETRIC] V =
||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||
WRITE R LITTLER V

@mixed USAPRICE  1  60:1 85:4    R   LITTLER   V
# USAPRICE{1 TO 2} USARGNP{1 TO 2} CONSTANT




C) Output.
source(noecho) I:\winrats\uhero\mixreg.src
cal 60 1 4
allocate 85:4
open data I:\winrats\usadata.rat
data(format=rats) /

* Using built-in procedure to do BVAR regression with Minnesota priors
COMPUTE GAMMA=0.2
COMPUTE FIJ=0.5
system 1 to 2
variables usaprice usargnp
lags 1 to 2
det constant
specify(type=symmetric,tight=GAMMA)  FIJ
end(system)


Summary of the Prior...
Tightness Parameter 0.200000
Harmonic Lag Decay with Parameter 0.000000
Standard Deviations as Fraction of Tightness and Prior Means
  Listed Under the Dependent Variable
          USAPRICE    USARGNP
USAPRICE  1.00000000 0.50000000
USARGNP   0.50000000 1.00000000
Mean      1.00000000 1.00000000

estimate

Dependent Variable USAPRICE - Estimation by Mixed Estimation
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom   101
Centered R**2     0.999907      R Bar **2   0.999907
Uncentered R**2   0.999984      T x R**2     101.998
Mean of Dependent Variable      53.205882353
Std Error of Dependent Variable 24.065162461
Standard Error of Estimate       0.231678752
Sum of Squared Residuals        5.4211794375
Durbin-Watson Statistic             2.032795

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  USAPRICE{1}               1.558718576  0.063276664     24.63339
0.00000000
2.  USAPRICE{2}              -0.564449553  0.062927823     -8.96979
0.00000000
3.  USARGNP{1}                0.000036688  0.000490931      0.07473
0.94057554
4.  USARGNP{2}                0.000506875  0.000501614      1.01049
0.31467619
5.  Constant                 -0.796232629  0.201750915     -3.94661
0.00014664

F-Tests, Dependent Variable USAPRICE
Variable            F-Statistic       Signif
USAPRICE              68851.8400     0.0000000
USARGNP                   8.8141     0.0002963


Dependent Variable USARGNP - Estimation by Mixed Estimation
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom   101
Centered R**2     0.997654      R Bar **2   0.997654
Uncentered R**2   0.999903      T x R**2     101.990
Mean of Dependent Variable      2639.7245098
Std Error of Dependent Variable  551.4344454
Standard Error of Estimate        26.7063979
Sum of Squared Residuals        72036.400834
Durbin-Watson Statistic             1.949370

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  USAPRICE{1}               -8.52617351   5.78265018     -1.47444
0.14347331
2.  USAPRICE{2}                8.88189778   5.75035220      1.54458
0.12557472
3.  USARGNP{1}                 1.16968123   0.07879125     14.84532
0.00000000
4.  USARGNP{2}                -0.17729213   0.07989428     -2.21908
0.02871856
5.  Constant                  23.73450138  22.32510528      1.06313
0.29025804

F-Tests, Dependent Variable USARGNP
Variable            F-Statistic       Signif
USAPRICE                  2.0012     0.1404944
USARGNP                2486.7562     0.0000000


* Mixed regression by hand

* Compute S1, the standard error of auto regression on equation 1
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USAPRICE
LINREG(CMOMENT) USAPRICE
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}

Dependent Variable USAPRICE - Estimation by Least Squares
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom    97
Centered R**2     0.999911      R Bar **2   0.999907
Uncentered R**2   0.999985      T x R**2     101.998
Mean of Dependent Variable      53.205882353
Std Error of Dependent Variable 24.065162461
Standard Error of Estimate       0.231605150
Sum of Squared Residuals        5.2031717209
Regression F(4,97)               272586.2337
Significance Level of F           0.00000000
Durbin-Watson Statistic             2.463235
Q(25-0)                            25.940142
Significance Level of Q           0.41079860

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  Constant                 -0.584689219  0.209530831     -2.79047
0.00633768
2.  USAPRICE{1}               1.702187514  0.073717462     23.09070
0.00000000
3.  USAPRICE{2}              -0.707202173  0.073306405     -9.64721
0.00000000
4.  USARGNP{1}                0.000080177  0.000845945      0.09478
0.92468698
5.  USARGNP{2}                0.000328262  0.000869452      0.37755
0.70658905


* Two alternative ways to calculate S1, one with Degree of Freedom T-K,
the other T-NDET
COMPUTE S1=SQRT(%SEESQ)
*COMPUTE TEST1=%RSS/(%NOBS-1)
*COMPUTE S1=SQRT(TEST1)
DISPLAY S1 %SEESQ
      0.23161       0.05364

* Compute S2, the standard error of auto regression on equation 2
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USARGNP
LINREG(CMOMENT) USARGNP
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}

Dependent Variable USARGNP - Estimation by Least Squares
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom    97
Centered R**2     0.997688      R Bar **2   0.997593
Uncentered R**2   0.999904      T x R**2     101.990
Mean of Dependent Variable      2639.7245098
Std Error of Dependent Variable  551.4344454
Standard Error of Estimate        27.0542379
Sum of Squared Residuals        70997.383388
Regression F(4,97)                10465.8241
Significance Level of F           0.00000000
Durbin-Watson Statistic             2.127956
Q(25-0)                            21.316421
Significance Level of Q           0.67483977

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  Constant                  11.62277727  24.47569471      0.47487
0.63594696
2.  USAPRICE{1}              -15.95218521   8.61107693     -1.85252
0.06699205
3.  USAPRICE{2}               16.26287458   8.56306055      1.89919
0.06051095
4.  USARGNP{1}                 1.22350624   0.09881640     12.38161
0.00000000
5.  USARGNP{2}                -0.22393299   0.10156234     -2.20488
0.02982563

COMPUTE S2=SQRT(%SEESQ)
*COMPUTE TEST2=%RSS/(%NOBS-1)
*COMPUTE S2=SQRT(TEST2)
DISPLAY S2 %SEESQ
     27.05424     731.93179

* Compute the prior information for mixed regression

COMPUTE [RECTANGULAR] R =
||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||

COMPUTE [VECTOR] LITTLER = ||1,0,0,0,0||
COMPUTE [SYMMETRIC] V =
||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||
WRITE R LITTLER V
      1.0000         0.0000         0.0000         0.0000         0.0000

      0.0000         1.0000         0.0000         0.0000         0.0000

      0.0000         0.0000       233.6238         0.0000         0.0000

      0.0000         0.0000         0.0000       233.6238         0.0000

      0.0000         0.0000         0.0000         0.0000         0.0000



      1.0000         0.0000         0.0000         0.0000         0.0000



      0.0400
      0.0000         0.0400
      0.0000         0.0000         0.0400
      0.0000         0.0000         0.0000         0.0400
      0.0000         0.0000         0.0000         0.0000         0.0400




@mixed USAPRICE  1  60:1 85:4    R   LITTLER   V
# USAPRICE{1 TO 2} USARGNP{1 TO 2} CONSTANT
      0.96040

Dependent Variable USAPRICE - Estimation by Least Squares
Quarterly Data From 60:01 To 85:04
Usable Observations    102      Degrees of Freedom    97
 Total Observations    104      Skipped/Missing        2
Centered R**2     0.999908      R Bar **2   0.999904
Uncentered R**2   0.999984      T x R**2     101.998
Mean of Dependent Variable      53.205882353
Std Error of Dependent Variable 24.065162461
Standard Error of Estimate       0.235824529
Sum of Squared Residuals        5.3944812376
Regression F(4,97)               262918.3940
Significance Level of F           0.00000000
Durbin-Watson Statistic             2.062554
Q(26-0)                            32.607800
Significance Level of Q           0.17378298

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  USAPRICE{1}               1.567767815  0.064966164     24.13207
0.00000000
2.  USAPRICE{2}              -0.573452845  0.064607630     -8.87593
0.00000000
3.  USARGNP{1}                0.000038387  0.000506590      0.07577
0.93975458
4.  USARGNP{2}                0.000496622  0.000517796      0.95911
0.33988919
5.  Constant                 -0.782826295  0.205787277     -3.80406
0.00024902

--------------E444FCC7106BBD4BFD6B362A
Content-Type: text/html; charset=us-ascii
Content-Transfer-Encoding: 7bit

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
<b>Hi:</b>
<p><b>&nbsp;&nbsp;&nbsp; I am a user of WINRATS 4.3. Lately I have been
trying to reproduce the result of</b>
<br><b>Bayesian VAR (with Minnesota prior) through a Mixed Regression program.
I am able</b>
<br><b>to get really close resemblance in the coefficients, however, they
are not identical. In</b>
<br><b>what follows, please find my program code and output. My main questions
are:</b>
<br><b>1) Does built-in BVAR procedure first demean variables?</b>
<br><b>2) If not, how to handle deterministic variables? Is my way correct?</b>
<br><b>3) What is the reason for close, however not identical, regression
coefficients?</b>
<p><b>&nbsp;&nbsp;&nbsp; I look forward to your response. Thank you very
much.</b>
<br><b>Allison</b>
<p><b>A) Code for mixreg.src ( identical to the example you give on page
5-13 of manual</b>
<br><b>version 4, except that I adjust the degree of freedom from T-K to
T-NDET with NDET</b>
<br><b>being number of deterministic variables)</b>
<p><font face="Courier New,Courier"><font size=-1>PROCEDURE MIXED DEPVAR
NDET NBEG NEND CAPR LOWR V</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; SERIES&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; REAL&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
NDET</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; INTEGER&nbsp;&nbsp;&nbsp;&nbsp;
NBEG&nbsp; NEND ; * Estimation Range</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; RECTANGULAR
CAPR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ; * R matrix: m x NREG</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; VECTOR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
LOWR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ; * r vector: m x 1</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; SYMMETRIC&nbsp;&nbsp;
V&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ; * V matrix: m
x m</font></font>
<br><font face="Courier New,Courier"><font size=-1>*</font></font>
<br><font face="Courier New,Courier"><font size=-1>LOCAL SYMMETRIC&nbsp;&nbsp;
XXMIXED</font></font>
<br><font face="Courier New,Courier"><font size=-1>LOCAL VECTOR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
XYMIXED</font></font>
<br><font face="Courier New,Courier"><font size=-1>LOCAL INDEX&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
REGSUPP&nbsp;&nbsp;&nbsp; ; * Array for supplementary card</font></font>
<br><font face="Courier New,Courier"><font size=-1>*</font></font>
<br><font face="Courier New,Courier"><font size=-1>ENTER(VARYING) REGSUPP&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
; * Bring in supplementary card</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT NBEG NEND&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
; * CMOM including depvar</font></font>
<br><font face="Courier New,Courier"><font size=-1># REGSUPP DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOM, NOPRINT)
DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1># REGSUPP</font></font>
<br><font face="Courier New,Courier"><font size=-1>OVERLAY&nbsp; %CMOM(1,1)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
WITH XXMIXED(%NREG,%NREG)</font></font>
<br><font face="Courier New,Courier"><font size=-1>OVERLAY&nbsp; %CMOM(%NREG+1,1)
WITH XYMIXED(%NREG)</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE ADJ=(%NOBS-%NREG)/(%NOBS-NDET)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY ADJ</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE XXMIXED=XXMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*CAPR)</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE XYMIXED=XYMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*LOWR)</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOM) DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1>#REGSUPP</font></font>
<br><font face="Courier New,Courier"><font size=-1>END</font></font>
<br>&nbsp;
<br>&nbsp;
<p><b>B) Program code for doing mixed estimation regression.</b>
<p><font face="Courier New,Courier"><font size=-1>source(noecho) I:\winrats\uhero\mixreg.src</font></font>
<br><font face="Courier New,Courier"><font size=-1>cal 60 1 4</font></font>
<br><font face="Courier New,Courier"><font size=-1>allocate 85:4</font></font>
<br><font face="Courier New,Courier"><font size=-1>open data I:\winrats\usadata.rat</font></font>
<br><font face="Courier New,Courier"><font size=-1>data(format=rats) /</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Using built-in procedure
to do BVAR regression with Minnesota priors</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE GAMMA=0.2</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE FIJ=0.5</font></font>
<br><font face="Courier New,Courier"><font size=-1>system 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>variables usaprice usargnp</font></font>
<br><font face="Courier New,Courier"><font size=-1>lags 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>det constant</font></font>
<br><font face="Courier New,Courier"><font size=-1>specify(type=symmetric,tight=GAMMA)&nbsp;
FIJ</font></font>
<br><font face="Courier New,Courier"><font size=-1>end(system)</font></font>
<br><font face="Courier New,Courier"><font size=-1>estimate</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Mixed regression by
hand</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S1, the standard
error of auto regression on equation 1</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Two alternative ways
to calculate S1, one with Degree of Freedom T-K,</font></font>
<br><font face="Courier New,Courier"><font size=-1>the other T-NDET</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE S1=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST1=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S1=SQRT(TEST1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S1 %SEESQ</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S2, the standard
error of auto regression on equation 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE S2=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST2=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S2=SQRT(TEST2)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S2 %SEESQ</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute the prior information
for mixed regression</font></font>
<p><font face="Courier New,Courier"><font size=-1>COMPUTE [RECTANGULAR]
R =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [VECTOR] LITTLER
= ||1,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [SYMMETRIC]
V =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||</font></font>
<br><font face="Courier New,Courier"><font size=-1>WRITE R LITTLER V</font></font>
<p><font face="Courier New,Courier"><font size=-1>@mixed USAPRICE&nbsp;
1&nbsp; 60:1 85:4&nbsp;&nbsp;&nbsp; R&nbsp;&nbsp; LITTLER&nbsp;&nbsp; V</font></font>
<br><font face="Courier New,Courier"><font size=-1># USAPRICE{1 TO 2} USARGNP{1
TO 2} CONSTANT</font></font>
<br>&nbsp;
<br>&nbsp;
<br>&nbsp;
<p><b>C) Output.</b>
<br><font face="Courier New,Courier"><font size=-1>source(noecho) I:\winrats\uhero\mixreg.src</font></font>
<br><font face="Courier New,Courier"><font size=-1>cal 60 1 4</font></font>
<br><font face="Courier New,Courier"><font size=-1>allocate 85:4</font></font>
<br><font face="Courier New,Courier"><font size=-1>open data I:\winrats\usadata.rat</font></font>
<br><font face="Courier New,Courier"><font size=-1>data(format=rats) /</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Using built-in procedure
to do BVAR regression with Minnesota priors</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE GAMMA=0.2</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE FIJ=0.5</font></font>
<br><font face="Courier New,Courier"><font size=-1>system 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>variables usaprice usargnp</font></font>
<br><font face="Courier New,Courier"><font size=-1>lags 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>det constant</font></font>
<br><font face="Courier New,Courier"><font size=-1>specify(type=symmetric,tight=GAMMA)&nbsp;
FIJ</font></font>
<br><font face="Courier New,Courier"><font size=-1>end(system)</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>Summary of the Prior...</font></font>
<br><font face="Courier New,Courier"><font size=-1>Tightness Parameter
0.200000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Harmonic Lag Decay with
Parameter 0.000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Deviations
as Fraction of Tightness and Prior Means</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp; Listed Under
the Dependent Variable</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
USAPRICE&nbsp;&nbsp;&nbsp; USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>USAPRICE&nbsp; 1.00000000
0.50000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>USARGNP&nbsp;&nbsp;
0.50000000 1.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.00000000 1.00000000</font></font>
<p><font face="Courier New,Courier"><font size=-1>estimate</font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USAPRICE
- Estimation by Mixed Estimation</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp; 101</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.999907&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.999907</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999984&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.998</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
53.205882353</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable 24.065162461</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.231678752</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.4211794375</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.032795</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.558718576&nbsp; 0.063276664&nbsp;&nbsp;&nbsp;&nbsp; 24.63339</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.564449553&nbsp; 0.062927823&nbsp;&nbsp;&nbsp;&nbsp; -8.96979</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000036688&nbsp; 0.000490931&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.07473</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.94057554</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000506875&nbsp; 0.000501614&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.01049</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.31467619</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.796232629&nbsp; 0.201750915&nbsp;&nbsp;&nbsp;&nbsp; -3.94661</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00014664</font></font>
<p><font face="Courier New,Courier"><font size=-1>F-Tests, Dependent Variable
USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1>Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
F-Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>USAPRICE&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
68851.8400&nbsp;&nbsp;&nbsp;&nbsp; 0.0000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>USARGNP&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
8.8141&nbsp;&nbsp;&nbsp;&nbsp; 0.0002963</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USARGNP
- Estimation by Mixed Estimation</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp; 101</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.997654&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.997654</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999903&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.990</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2639.7245098</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable&nbsp; 551.4344454</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
26.7063979</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
72036.400834</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.949370</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-8.52617351&nbsp;&nbsp; 5.78265018&nbsp;&nbsp;&nbsp;&nbsp; -1.47444</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.14347331</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
8.88189778&nbsp;&nbsp; 5.75035220&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.54458</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.12557472</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.16968123&nbsp;&nbsp; 0.07879125&nbsp;&nbsp;&nbsp;&nbsp; 14.84532</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.17729213&nbsp;&nbsp; 0.07989428&nbsp;&nbsp;&nbsp;&nbsp; -2.21908</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.02871856</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
23.73450138&nbsp; 22.32510528&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.06313</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.29025804</font></font>
<p><font face="Courier New,Courier"><font size=-1>F-Tests, Dependent Variable
USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
F-Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>USAPRICE&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.0012&nbsp;&nbsp;&nbsp;&nbsp; 0.1404944</font></font>
<br><font face="Courier New,Courier"><font size=-1>USARGNP&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2486.7562&nbsp;&nbsp;&nbsp;&nbsp; 0.0000000</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>* Mixed regression by
hand</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S1, the standard
error of auto regression on equation 1</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USAPRICE
- Estimation by Least Squares</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp;&nbsp;
97</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.999911&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.999907</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999985&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.998</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
53.205882353</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable 24.065162461</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.231605150</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.2031717209</font></font>
<br><font face="Courier New,Courier"><font size=-1>Regression F(4,97)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
272586.2337</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
F&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.463235</font></font>
<br><font face="Courier New,Courier"><font size=-1>Q(25-0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
25.940142</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
Q&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.41079860</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.584689219&nbsp; 0.209530831&nbsp;&nbsp;&nbsp;&nbsp; -2.79047</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00633768</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.702187514&nbsp; 0.073717462&nbsp;&nbsp;&nbsp;&nbsp; 23.09070</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.707202173&nbsp; 0.073306405&nbsp;&nbsp;&nbsp;&nbsp; -9.64721</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000080177&nbsp; 0.000845945&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.09478</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.92468698</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000328262&nbsp; 0.000869452&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.37755</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.70658905</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>* Two alternative ways
to calculate S1, one with Degree of Freedom T-K,</font></font>
<br><font face="Courier New,Courier"><font size=-1>the other T-NDET</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE S1=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST1=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S1=SQRT(TEST1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S1 %SEESQ</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.23161&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.05364</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S2, the standard
error of auto regression on equation 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USARGNP
- Estimation by Least Squares</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp;&nbsp;
97</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.997688&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.997593</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999904&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.990</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2639.7245098</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable&nbsp; 551.4344454</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
27.0542379</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
70997.383388</font></font>
<br><font face="Courier New,Courier"><font size=-1>Regression F(4,97)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
10465.8241</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
F&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.127956</font></font>
<br><font face="Courier New,Courier"><font size=-1>Q(25-0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
21.316421</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
Q&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.67483977</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
11.62277727&nbsp; 24.47569471&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.47487</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.63594696</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-15.95218521&nbsp;&nbsp; 8.61107693&nbsp;&nbsp;&nbsp;&nbsp; -1.85252</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.06699205</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
16.26287458&nbsp;&nbsp; 8.56306055&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.89919</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.06051095</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.22350624&nbsp;&nbsp; 0.09881640&nbsp;&nbsp;&nbsp;&nbsp; 12.38161</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.22393299&nbsp;&nbsp; 0.10156234&nbsp;&nbsp;&nbsp;&nbsp; -2.20488</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.02982563</font></font>
<p><font face="Courier New,Courier"><font size=-1>COMPUTE S2=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST2=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S2=SQRT(TEST2)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S2 %SEESQ</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;
27.05424&nbsp;&nbsp;&nbsp;&nbsp; 731.93179</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute the prior information
for mixed regression</font></font>
<p><font face="Courier New,Courier"><font size=-1>COMPUTE [RECTANGULAR]
R =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [VECTOR] LITTLER
= ||1,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [SYMMETRIC]
V =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||</font></font>
<br><font face="Courier New,Courier"><font size=-1>WRITE R LITTLER V</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
233.6238&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 233.6238&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0400</font></font>
<br>&nbsp;
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>@mixed USAPRICE&nbsp;
1&nbsp; 60:1 85:4&nbsp;&nbsp;&nbsp; R&nbsp;&nbsp; LITTLER&nbsp;&nbsp; V</font></font>
<br><font face="Courier New,Courier"><font size=-1># USAPRICE{1 TO 2} USARGNP{1
TO 2} CONSTANT</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.96040</font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USAPRICE
- Estimation by Least Squares</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:01 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp;&nbsp;
97</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;Total Observations&nbsp;&nbsp;&nbsp;
104&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Skipped/Missing&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.999908&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.999904</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999984&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.998</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
53.205882353</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable 24.065162461</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.235824529</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.3944812376</font></font>
<br><font face="Courier New,Courier"><font size=-1>Regression F(4,97)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
262918.3940</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
F&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.062554</font></font>
<br><font face="Courier New,Courier"><font size=-1>Q(26-0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
32.607800</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
Q&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.17378298</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat&nbsp;&nbsp;&nbsp; Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.567767815&nbsp; 0.064966164&nbsp;&nbsp;&nbsp;&nbsp; 24.13207 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.573452845&nbsp; 0.064607630&nbsp;&nbsp;&nbsp;&nbsp; -8.87593 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000038387&nbsp; 0.000506590&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.07577 0.93975458</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000496622&nbsp; 0.000517796&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.95911 0.33988919</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.782826295&nbsp; 0.205787277&nbsp;&nbsp;&nbsp;&nbsp; -3.80406 0.00024902</font></font></html>

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From: Allison <tzhou@hawaii.edu>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: question about BVAR
Date: Tue, 20 Jun 2000 20:49:06 -1000
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Hi:

    I am a user of WINRATS 4.3. Lately I have been trying to reproduce
the result of
Bayesian VAR (with Minnesota prior) through a Mixed Regression program.
I am able
to get really close resemblance in the coefficients, however, they are
not identical. In
what follows, please find my program code and output. My main questions
are:
1) Does built-in BVAR procedure first demean variables?
2) If not, how to handle deterministic variables? Is my way correct?
3) What is the reason for close, however not identical, regression
coefficients?

    I look forward to your response. Thank you very much.
Allison

A) Code for mixreg.src ( identical to the example on page 5-13 of manual

version 4, except that I adjust the degree of freedom from T-K to T-NDET
with NDET
being number of deterministic variables)

PROCEDURE MIXED DEPVAR NDET NBEG NEND CAPR LOWR V
TYPE  SERIES      DEPVAR
TYPE  REAL        NDET
TYPE  INTEGER     NBEG  NEND ; * Estimation Range
TYPE  RECTANGULAR CAPR       ; * R matrix: m x NREG
TYPE  VECTOR      LOWR       ; * r vector: m x 1
TYPE  SYMMETRIC   V          ; * V matrix: m x m
*
LOCAL SYMMETRIC   XXMIXED
LOCAL VECTOR      XYMIXED
LOCAL INDEX       REGSUPP    ; * Array for supplementary card
*
ENTER(VARYING) REGSUPP       ; * Bring in supplementary card
CMOMENT NBEG NEND            ; * CMOM including depvar
# REGSUPP DEPVAR
LINREG(CMOM, NOPRINT) DEPVAR
# REGSUPP
OVERLAY  %CMOM(1,1)       WITH XXMIXED(%NREG,%NREG)
OVERLAY  %CMOM(%NREG+1,1) WITH XYMIXED(%NREG)
COMPUTE ADJ=(%NOBS-%NREG)/(%NOBS-NDET)
DISPLAY ADJ
COMPUTE XXMIXED=XXMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*CAPR)
COMPUTE XYMIXED=XYMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*LOWR)
LINREG(CMOM) DEPVAR
#REGSUPP
END



B) Program code for doing mixed estimation regression.

source(noecho) I:\winrats\uhero\mixreg.src
cal 60 1 4
allocate 85:4
open data I:\winrats\usadata.rat
data(format=rats) /

* Using built-in procedure to do BVAR regression with Minnesota priors
COMPUTE GAMMA=0.2
COMPUTE FIJ=0.5
system 1 to 2
variables usaprice usargnp
lags 1 to 2
det constant
specify(type=symmetric,tight=GAMMA)  FIJ
end(system)
estimate

* Mixed regression by hand

* Compute S1, the standard error of auto regression on equation 1
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USAPRICE
LINREG(CMOMENT) USAPRICE
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}

* Two alternative ways to calculate S1, one with Degree of Freedom T-K,
the other T-NDET
COMPUTE S1=SQRT(%SEESQ)
*COMPUTE TEST1=%RSS/(%NOBS-1)
*COMPUTE S1=SQRT(TEST1)
DISPLAY S1 %SEESQ

* Compute S2, the standard error of auto regression on equation 2
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USARGNP
LINREG(CMOMENT) USARGNP
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}
COMPUTE S2=SQRT(%SEESQ)
*COMPUTE TEST2=%RSS/(%NOBS-1)
*COMPUTE S2=SQRT(TEST2)
DISPLAY S2 %SEESQ

* Compute the prior information for mixed regression

COMPUTE [RECTANGULAR] R =
||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||

COMPUTE [VECTOR] LITTLER = ||1,0,0,0,0||
COMPUTE [SYMMETRIC] V =
||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||
WRITE R LITTLER V

@mixed USAPRICE  1  60:1 85:4    R   LITTLER   V
# USAPRICE{1 TO 2} USARGNP{1 TO 2} CONSTANT




C) Output.
source(noecho) I:\winrats\uhero\mixreg.src
cal 60 1 4
allocate 85:4
open data I:\winrats\usadata.rat
data(format=rats) /

* Using built-in procedure to do BVAR regression with Minnesota priors
COMPUTE GAMMA=0.2
COMPUTE FIJ=0.5
system 1 to 2
variables usaprice usargnp
lags 1 to 2
det constant
specify(type=symmetric,tight=GAMMA)  FIJ
end(system)


Summary of the Prior...
Tightness Parameter 0.200000
Harmonic Lag Decay with Parameter 0.000000
Standard Deviations as Fraction of Tightness and Prior Means
  Listed Under the Dependent Variable
          USAPRICE    USARGNP
USAPRICE  1.00000000 0.50000000
USARGNP   0.50000000 1.00000000
Mean      1.00000000 1.00000000

estimate

Dependent Variable USAPRICE - Estimation by Mixed Estimation
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom   101
Centered R**2     0.999907      R Bar **2   0.999907
Uncentered R**2   0.999984      T x R**2     101.998
Mean of Dependent Variable      53.205882353
Std Error of Dependent Variable 24.065162461
Standard Error of Estimate       0.231678752
Sum of Squared Residuals        5.4211794375
Durbin-Watson Statistic             2.032795

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  USAPRICE{1}               1.558718576  0.063276664     24.63339
0.00000000
2.  USAPRICE{2}              -0.564449553  0.062927823     -8.96979
0.00000000
3.  USARGNP{1}                0.000036688  0.000490931      0.07473
0.94057554
4.  USARGNP{2}                0.000506875  0.000501614      1.01049
0.31467619
5.  Constant                 -0.796232629  0.201750915     -3.94661
0.00014664

F-Tests, Dependent Variable USAPRICE
Variable            F-Statistic       Signif
USAPRICE              68851.8400     0.0000000
USARGNP                   8.8141     0.0002963


Dependent Variable USARGNP - Estimation by Mixed Estimation
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom   101
Centered R**2     0.997654      R Bar **2   0.997654
Uncentered R**2   0.999903      T x R**2     101.990
Mean of Dependent Variable      2639.7245098
Std Error of Dependent Variable  551.4344454
Standard Error of Estimate        26.7063979
Sum of Squared Residuals        72036.400834
Durbin-Watson Statistic             1.949370

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  USAPRICE{1}               -8.52617351   5.78265018     -1.47444
0.14347331
2.  USAPRICE{2}                8.88189778   5.75035220      1.54458
0.12557472
3.  USARGNP{1}                 1.16968123   0.07879125     14.84532
0.00000000
4.  USARGNP{2}                -0.17729213   0.07989428     -2.21908
0.02871856
5.  Constant                  23.73450138  22.32510528      1.06313
0.29025804

F-Tests, Dependent Variable USARGNP
Variable            F-Statistic       Signif
USAPRICE                  2.0012     0.1404944
USARGNP                2486.7562     0.0000000


* Mixed regression by hand

* Compute S1, the standard error of auto regression on equation 1
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USAPRICE
LINREG(CMOMENT) USAPRICE
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}

Dependent Variable USAPRICE - Estimation by Least Squares
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom    97
Centered R**2     0.999911      R Bar **2   0.999907
Uncentered R**2   0.999985      T x R**2     101.998
Mean of Dependent Variable      53.205882353
Std Error of Dependent Variable 24.065162461
Standard Error of Estimate       0.231605150
Sum of Squared Residuals        5.2031717209
Regression F(4,97)               272586.2337
Significance Level of F           0.00000000
Durbin-Watson Statistic             2.463235
Q(25-0)                            25.940142
Significance Level of Q           0.41079860

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  Constant                 -0.584689219  0.209530831     -2.79047
0.00633768
2.  USAPRICE{1}               1.702187514  0.073717462     23.09070
0.00000000
3.  USAPRICE{2}              -0.707202173  0.073306405     -9.64721
0.00000000
4.  USARGNP{1}                0.000080177  0.000845945      0.09478
0.92468698
5.  USARGNP{2}                0.000328262  0.000869452      0.37755
0.70658905


* Two alternative ways to calculate S1, one with Degree of Freedom T-K,
the other T-NDET
COMPUTE S1=SQRT(%SEESQ)
*COMPUTE TEST1=%RSS/(%NOBS-1)
*COMPUTE S1=SQRT(TEST1)
DISPLAY S1 %SEESQ
      0.23161       0.05364

* Compute S2, the standard error of auto regression on equation 2
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USARGNP
LINREG(CMOMENT) USARGNP
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}

Dependent Variable USARGNP - Estimation by Least Squares
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom    97
Centered R**2     0.997688      R Bar **2   0.997593
Uncentered R**2   0.999904      T x R**2     101.990
Mean of Dependent Variable      2639.7245098
Std Error of Dependent Variable  551.4344454
Standard Error of Estimate        27.0542379
Sum of Squared Residuals        70997.383388
Regression F(4,97)                10465.8241
Significance Level of F           0.00000000
Durbin-Watson Statistic             2.127956
Q(25-0)                            21.316421
Significance Level of Q           0.67483977

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  Constant                  11.62277727  24.47569471      0.47487
0.63594696
2.  USAPRICE{1}              -15.95218521   8.61107693     -1.85252
0.06699205
3.  USAPRICE{2}               16.26287458   8.56306055      1.89919
0.06051095
4.  USARGNP{1}                 1.22350624   0.09881640     12.38161
0.00000000
5.  USARGNP{2}                -0.22393299   0.10156234     -2.20488
0.02982563

COMPUTE S2=SQRT(%SEESQ)
*COMPUTE TEST2=%RSS/(%NOBS-1)
*COMPUTE S2=SQRT(TEST2)
DISPLAY S2 %SEESQ
     27.05424     731.93179

* Compute the prior information for mixed regression

COMPUTE [RECTANGULAR] R =
||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||

COMPUTE [VECTOR] LITTLER = ||1,0,0,0,0||
COMPUTE [SYMMETRIC] V =
||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||
WRITE R LITTLER V
      1.0000         0.0000         0.0000         0.0000         0.0000

      0.0000         1.0000         0.0000         0.0000         0.0000

      0.0000         0.0000       233.6238         0.0000         0.0000

      0.0000         0.0000         0.0000       233.6238         0.0000

      0.0000         0.0000         0.0000         0.0000         0.0000



      1.0000         0.0000         0.0000         0.0000         0.0000



      0.0400
      0.0000         0.0400
      0.0000         0.0000         0.0400
      0.0000         0.0000         0.0000         0.0400
      0.0000         0.0000         0.0000         0.0000         0.0400




@mixed USAPRICE  1  60:1 85:4    R   LITTLER   V
# USAPRICE{1 TO 2} USARGNP{1 TO 2} CONSTANT
      0.96040

Dependent Variable USAPRICE - Estimation by Least Squares
Quarterly Data From 60:01 To 85:04
Usable Observations    102      Degrees of Freedom    97
 Total Observations    104      Skipped/Missing        2
Centered R**2     0.999908      R Bar **2   0.999904
Uncentered R**2   0.999984      T x R**2     101.998
Mean of Dependent Variable      53.205882353
Std Error of Dependent Variable 24.065162461
Standard Error of Estimate       0.235824529
Sum of Squared Residuals        5.3944812376
Regression F(4,97)               262918.3940
Significance Level of F           0.00000000
Durbin-Watson Statistic             2.062554
Q(26-0)                            32.607800
Significance Level of Q           0.17378298

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  USAPRICE{1}               1.567767815  0.064966164     24.13207
0.00000000
2.  USAPRICE{2}              -0.573452845  0.064607630     -8.87593
0.00000000
3.  USARGNP{1}                0.000038387  0.000506590      0.07577
0.93975458
4.  USARGNP{2}                0.000496622  0.000517796      0.95911
0.33988919
5.  Constant                 -0.782826295  0.205787277     -3.80406
0.00024902

--------------B977848CA3CDD97EA1E5FB95
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<html>
&nbsp;
<br><b>Hi:</b><b></b>
<p><b>&nbsp;&nbsp;&nbsp; I am a user of WINRATS 4.3. Lately I have been
trying to reproduce the result of</b>
<br><b>Bayesian VAR (with Minnesota prior) through a Mixed Regression program.
I am able</b>
<br><b>to get really close resemblance in the coefficients, however, they
are not identical. In</b>
<br><b>what follows, please find my program code and output. My main questions
are:</b>
<br><b>1) Does built-in BVAR procedure first demean variables?</b>
<br><b>2) If not, how to handle deterministic variables? Is my way correct?</b>
<br><b>3) What is the reason for close, however not identical, regression
coefficients?</b><b></b>
<p><b>&nbsp;&nbsp;&nbsp; I look forward to your response. Thank you very
much.</b>
<br><b>Allison</b><b></b>
<p><b>A) Code for mixreg.src ( identical to the example on page 5-13 of
manual</b>
<br><b>version 4, except that I adjust the degree of freedom from T-K to
T-NDET with NDET</b>
<br><b>being number of deterministic variables)</b>
<p><font face="Courier New,Courier"><font size=-1>PROCEDURE MIXED DEPVAR
NDET NBEG NEND CAPR LOWR V</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; SERIES&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; REAL&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
NDET</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; INTEGER&nbsp;&nbsp;&nbsp;&nbsp;
NBEG&nbsp; NEND ; * Estimation Range</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; RECTANGULAR
CAPR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ; * R matrix: m x NREG</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; VECTOR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
LOWR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ; * r vector: m x 1</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; SYMMETRIC&nbsp;&nbsp;
V&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ; * V matrix: m
x m</font></font>
<br><font face="Courier New,Courier"><font size=-1>*</font></font>
<br><font face="Courier New,Courier"><font size=-1>LOCAL SYMMETRIC&nbsp;&nbsp;
XXMIXED</font></font>
<br><font face="Courier New,Courier"><font size=-1>LOCAL VECTOR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
XYMIXED</font></font>
<br><font face="Courier New,Courier"><font size=-1>LOCAL INDEX&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
REGSUPP&nbsp;&nbsp;&nbsp; ; * Array for supplementary card</font></font>
<br><font face="Courier New,Courier"><font size=-1>*</font></font>
<br><font face="Courier New,Courier"><font size=-1>ENTER(VARYING) REGSUPP&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
; * Bring in supplementary card</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT NBEG NEND&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
; * CMOM including depvar</font></font>
<br><font face="Courier New,Courier"><font size=-1># REGSUPP DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOM, NOPRINT)
DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1># REGSUPP</font></font>
<br><font face="Courier New,Courier"><font size=-1>OVERLAY&nbsp; %CMOM(1,1)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
WITH XXMIXED(%NREG,%NREG)</font></font>
<br><font face="Courier New,Courier"><font size=-1>OVERLAY&nbsp; %CMOM(%NREG+1,1)
WITH XYMIXED(%NREG)</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE ADJ=(%NOBS-%NREG)/(%NOBS-NDET)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY ADJ</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE XXMIXED=XXMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*CAPR)</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE XYMIXED=XYMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*LOWR)</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOM) DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1>#REGSUPP</font></font>
<br><font face="Courier New,Courier"><font size=-1>END</font></font>
<br>&nbsp;
<br>&nbsp;
<p><b>B) Program code for doing mixed estimation regression.</b>
<p><font face="Courier New,Courier"><font size=-1>source(noecho) I:\winrats\uhero\mixreg.src</font></font>
<br><font face="Courier New,Courier"><font size=-1>cal 60 1 4</font></font>
<br><font face="Courier New,Courier"><font size=-1>allocate 85:4</font></font>
<br><font face="Courier New,Courier"><font size=-1>open data I:\winrats\usadata.rat</font></font>
<br><font face="Courier New,Courier"><font size=-1>data(format=rats) /</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Using built-in procedure
to do BVAR regression with Minnesota priors</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE GAMMA=0.2</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE FIJ=0.5</font></font>
<br><font face="Courier New,Courier"><font size=-1>system 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>variables usaprice usargnp</font></font>
<br><font face="Courier New,Courier"><font size=-1>lags 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>det constant</font></font>
<br><font face="Courier New,Courier"><font size=-1>specify(type=symmetric,tight=GAMMA)&nbsp;
FIJ</font></font>
<br><font face="Courier New,Courier"><font size=-1>end(system)</font></font>
<br><font face="Courier New,Courier"><font size=-1>estimate</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Mixed regression by
hand</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S1, the standard
error of auto regression on equation 1</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Two alternative ways
to calculate S1, one with Degree of Freedom T-K,</font></font>
<br><font face="Courier New,Courier"><font size=-1>the other T-NDET</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE S1=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST1=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S1=SQRT(TEST1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S1 %SEESQ</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S2, the standard
error of auto regression on equation 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE S2=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST2=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S2=SQRT(TEST2)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S2 %SEESQ</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute the prior information
for mixed regression</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>COMPUTE [RECTANGULAR]
R =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [VECTOR] LITTLER
= ||1,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [SYMMETRIC]
V =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||</font></font>
<br><font face="Courier New,Courier"><font size=-1>WRITE R LITTLER V</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>@mixed USAPRICE&nbsp;
1&nbsp; 60:1 85:4&nbsp;&nbsp;&nbsp; R&nbsp;&nbsp; LITTLER&nbsp;&nbsp; V</font></font>
<br><font face="Courier New,Courier"><font size=-1># USAPRICE{1 TO 2} USARGNP{1
TO 2} CONSTANT</font></font>
<br>&nbsp;
<br>&nbsp;
<br>&nbsp;
<p><b>C) Output.</b>
<br><font face="Courier New,Courier"><font size=-1>source(noecho) I:\winrats\uhero\mixreg.src</font></font>
<br><font face="Courier New,Courier"><font size=-1>cal 60 1 4</font></font>
<br><font face="Courier New,Courier"><font size=-1>allocate 85:4</font></font>
<br><font face="Courier New,Courier"><font size=-1>open data I:\winrats\usadata.rat</font></font>
<br><font face="Courier New,Courier"><font size=-1>data(format=rats) /</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Using built-in procedure
to do BVAR regression with Minnesota priors</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE GAMMA=0.2</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE FIJ=0.5</font></font>
<br><font face="Courier New,Courier"><font size=-1>system 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>variables usaprice usargnp</font></font>
<br><font face="Courier New,Courier"><font size=-1>lags 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>det constant</font></font>
<br><font face="Courier New,Courier"><font size=-1>specify(type=symmetric,tight=GAMMA)&nbsp;
FIJ</font></font>
<br><font face="Courier New,Courier"><font size=-1>end(system)</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>Summary of the Prior...</font></font>
<br><font face="Courier New,Courier"><font size=-1>Tightness Parameter
0.200000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Harmonic Lag Decay with
Parameter 0.000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Deviations
as Fraction of Tightness and Prior Means</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp; Listed Under
the Dependent Variable</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
USAPRICE&nbsp;&nbsp;&nbsp; USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>USAPRICE&nbsp; 1.00000000
0.50000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>USARGNP&nbsp;&nbsp;
0.50000000 1.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.00000000 1.00000000</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>estimate</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USAPRICE
- Estimation by Mixed Estimation</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp; 101</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.999907&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.999907</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999984&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.998</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
53.205882353</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable 24.065162461</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.231678752</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.4211794375</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.032795</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.558718576&nbsp; 0.063276664&nbsp;&nbsp;&nbsp;&nbsp; 24.63339</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.564449553&nbsp; 0.062927823&nbsp;&nbsp;&nbsp;&nbsp; -8.96979</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000036688&nbsp; 0.000490931&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.07473</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.94057554</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000506875&nbsp; 0.000501614&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.01049</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.31467619</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.796232629&nbsp; 0.201750915&nbsp;&nbsp;&nbsp;&nbsp; -3.94661</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00014664</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>F-Tests, Dependent Variable
USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1>Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
F-Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>USAPRICE&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
68851.8400&nbsp;&nbsp;&nbsp;&nbsp; 0.0000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>USARGNP&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
8.8141&nbsp;&nbsp;&nbsp;&nbsp; 0.0002963</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USARGNP
- Estimation by Mixed Estimation</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp; 101</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.997654&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.997654</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999903&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.990</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2639.7245098</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable&nbsp; 551.4344454</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
26.7063979</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
72036.400834</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.949370</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-8.52617351&nbsp;&nbsp; 5.78265018&nbsp;&nbsp;&nbsp;&nbsp; -1.47444</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.14347331</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
8.88189778&nbsp;&nbsp; 5.75035220&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.54458</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.12557472</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.16968123&nbsp;&nbsp; 0.07879125&nbsp;&nbsp;&nbsp;&nbsp; 14.84532</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.17729213&nbsp;&nbsp; 0.07989428&nbsp;&nbsp;&nbsp;&nbsp; -2.21908</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.02871856</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
23.73450138&nbsp; 22.32510528&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.06313</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.29025804</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>F-Tests, Dependent Variable
USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
F-Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>USAPRICE&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.0012&nbsp;&nbsp;&nbsp;&nbsp; 0.1404944</font></font>
<br><font face="Courier New,Courier"><font size=-1>USARGNP&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2486.7562&nbsp;&nbsp;&nbsp;&nbsp; 0.0000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Mixed regression by
hand</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S1, the standard
error of auto regression on equation 1</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USAPRICE
- Estimation by Least Squares</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp;&nbsp;
97</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.999911&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.999907</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999985&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.998</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
53.205882353</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable 24.065162461</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.231605150</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.2031717209</font></font>
<br><font face="Courier New,Courier"><font size=-1>Regression F(4,97)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
272586.2337</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
F&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.463235</font></font>
<br><font face="Courier New,Courier"><font size=-1>Q(25-0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
25.940142</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
Q&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.41079860</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.584689219&nbsp; 0.209530831&nbsp;&nbsp;&nbsp;&nbsp; -2.79047</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00633768</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.702187514&nbsp; 0.073717462&nbsp;&nbsp;&nbsp;&nbsp; 23.09070</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.707202173&nbsp; 0.073306405&nbsp;&nbsp;&nbsp;&nbsp; -9.64721</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000080177&nbsp; 0.000845945&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.09478</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.92468698</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000328262&nbsp; 0.000869452&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.37755</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.70658905</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Two alternative ways
to calculate S1, one with Degree of Freedom T-K,</font></font>
<br><font face="Courier New,Courier"><font size=-1>the other T-NDET</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE S1=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST1=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S1=SQRT(TEST1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S1 %SEESQ</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.23161&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.05364</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S2, the standard
error of auto regression on equation 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USARGNP
- Estimation by Least Squares</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp;&nbsp;
97</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.997688&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.997593</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999904&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.990</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2639.7245098</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable&nbsp; 551.4344454</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
27.0542379</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
70997.383388</font></font>
<br><font face="Courier New,Courier"><font size=-1>Regression F(4,97)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
10465.8241</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
F&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.127956</font></font>
<br><font face="Courier New,Courier"><font size=-1>Q(25-0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
21.316421</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
Q&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.67483977</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
11.62277727&nbsp; 24.47569471&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.47487</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.63594696</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-15.95218521&nbsp;&nbsp; 8.61107693&nbsp;&nbsp;&nbsp;&nbsp; -1.85252</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.06699205</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
16.26287458&nbsp;&nbsp; 8.56306055&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.89919</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.06051095</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.22350624&nbsp;&nbsp; 0.09881640&nbsp;&nbsp;&nbsp;&nbsp; 12.38161</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.22393299&nbsp;&nbsp; 0.10156234&nbsp;&nbsp;&nbsp;&nbsp; -2.20488</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.02982563</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>COMPUTE S2=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST2=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S2=SQRT(TEST2)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S2 %SEESQ</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;
27.05424&nbsp;&nbsp;&nbsp;&nbsp; 731.93179</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute the prior information
for mixed regression</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>COMPUTE [RECTANGULAR]
R =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [VECTOR] LITTLER
= ||1,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [SYMMETRIC]
V =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||</font></font>
<br><font face="Courier New,Courier"><font size=-1>WRITE R LITTLER V</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
233.6238&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 233.6238&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>@mixed USAPRICE&nbsp;
1&nbsp; 60:1 85:4&nbsp;&nbsp;&nbsp; R&nbsp;&nbsp; LITTLER&nbsp;&nbsp; V</font></font>
<br><font face="Courier New,Courier"><font size=-1># USAPRICE{1 TO 2} USARGNP{1
TO 2} CONSTANT</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.96040</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USAPRICE
- Estimation by Least Squares</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:01 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp;&nbsp;
97</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;Total Observations&nbsp;&nbsp;&nbsp;
104&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Skipped/Missing&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.999908&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.999904</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999984&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.998</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
53.205882353</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable 24.065162461</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.235824529</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.3944812376</font></font>
<br><font face="Courier New,Courier"><font size=-1>Regression F(4,97)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
262918.3940</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
F&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.062554</font></font>
<br><font face="Courier New,Courier"><font size=-1>Q(26-0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
32.607800</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
Q&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.17378298</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font><font face="Courier New,Courier"><font size=-1></font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.567767815&nbsp; 0.064966164&nbsp;&nbsp;&nbsp;&nbsp; 24.13207</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.573452845&nbsp; 0.064607630&nbsp;&nbsp;&nbsp;&nbsp; -8.87593</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000038387&nbsp; 0.000506590&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.07577</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.93975458</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000496622&nbsp; 0.000517796&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.95911</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.33988919</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.782826295&nbsp; 0.205787277&nbsp;&nbsp;&nbsp;&nbsp; -3.80406</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00024902</font></font></html>

--------------B977848CA3CDD97EA1E5FB95--


---------- End of message ----------

From: Allison <tzhou@hawaii.edu>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: [Fwd: question about BVAR]
Date: Tue, 20 Jun 2000 21:25:36 -1000
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From: Allison <tzhou@hawaii.edu>
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Subject: question about BVAR
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Hi:

    I am a user of WINRATS 4.3. Lately I have been trying to reproduce
the result of
Bayesian VAR (with Minnesota prior) through a Mixed Regression program.
I am able
to get really close resemblance in the coefficients, however, they are
not identical. In
what follows, please find my program code and output. My main questions
are:
1) Does built-in BVAR procedure first demean variables?
2) If not, how to handle deterministic variables? Is my way correct?
3) What is the reason for close, however not identical, regression
coefficients?

    I look forward to your response. Thank you very much.
Allison

A) Code for mixreg.src ( identical to the example you give on page 5-13
of manual
version 4, except that I adjust the degree of freedom from T-K to T-NDET
with NDET
being number of deterministic variables)

PROCEDURE MIXED DEPVAR NDET NBEG NEND CAPR LOWR V
TYPE  SERIES      DEPVAR
TYPE  REAL        NDET
TYPE  INTEGER     NBEG  NEND ; * Estimation Range
TYPE  RECTANGULAR CAPR       ; * R matrix: m x NREG
TYPE  VECTOR      LOWR       ; * r vector: m x 1
TYPE  SYMMETRIC   V          ; * V matrix: m x m
*
LOCAL SYMMETRIC   XXMIXED
LOCAL VECTOR      XYMIXED
LOCAL INDEX       REGSUPP    ; * Array for supplementary card
*
ENTER(VARYING) REGSUPP       ; * Bring in supplementary card
CMOMENT NBEG NEND            ; * CMOM including depvar
# REGSUPP DEPVAR
LINREG(CMOM, NOPRINT) DEPVAR
# REGSUPP
OVERLAY  %CMOM(1,1)       WITH XXMIXED(%NREG,%NREG)
OVERLAY  %CMOM(%NREG+1,1) WITH XYMIXED(%NREG)
COMPUTE ADJ=(%NOBS-%NREG)/(%NOBS-NDET)
DISPLAY ADJ
COMPUTE XXMIXED=XXMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*CAPR)
COMPUTE XYMIXED=XYMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*LOWR)
LINREG(CMOM) DEPVAR
#REGSUPP
END



B) Program code for doing mixed estimation regression.

source(noecho) I:\winrats\uhero\mixreg.src
cal 60 1 4
allocate 85:4
open data I:\winrats\usadata.rat
data(format=rats) /

* Using built-in procedure to do BVAR regression with Minnesota priors
COMPUTE GAMMA=0.2
COMPUTE FIJ=0.5
system 1 to 2
variables usaprice usargnp
lags 1 to 2
det constant
specify(type=symmetric,tight=GAMMA)  FIJ
end(system)
estimate

* Mixed regression by hand

* Compute S1, the standard error of auto regression on equation 1
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USAPRICE
LINREG(CMOMENT) USAPRICE
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}

* Two alternative ways to calculate S1, one with Degree of Freedom T-K,
the other T-NDET
COMPUTE S1=SQRT(%SEESQ)
*COMPUTE TEST1=%RSS/(%NOBS-1)
*COMPUTE S1=SQRT(TEST1)
DISPLAY S1 %SEESQ

* Compute S2, the standard error of auto regression on equation 2
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USARGNP
LINREG(CMOMENT) USARGNP
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}
COMPUTE S2=SQRT(%SEESQ)
*COMPUTE TEST2=%RSS/(%NOBS-1)
*COMPUTE S2=SQRT(TEST2)
DISPLAY S2 %SEESQ

* Compute the prior information for mixed regression

COMPUTE [RECTANGULAR] R =
||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||

COMPUTE [VECTOR] LITTLER = ||1,0,0,0,0||
COMPUTE [SYMMETRIC] V =
||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||
WRITE R LITTLER V

@mixed USAPRICE  1  60:1 85:4    R   LITTLER   V
# USAPRICE{1 TO 2} USARGNP{1 TO 2} CONSTANT




C) Output.
source(noecho) I:\winrats\uhero\mixreg.src
cal 60 1 4
allocate 85:4
open data I:\winrats\usadata.rat
data(format=rats) /

* Using built-in procedure to do BVAR regression with Minnesota priors
COMPUTE GAMMA=0.2
COMPUTE FIJ=0.5
system 1 to 2
variables usaprice usargnp
lags 1 to 2
det constant
specify(type=symmetric,tight=GAMMA)  FIJ
end(system)


Summary of the Prior...
Tightness Parameter 0.200000
Harmonic Lag Decay with Parameter 0.000000
Standard Deviations as Fraction of Tightness and Prior Means
  Listed Under the Dependent Variable
          USAPRICE    USARGNP
USAPRICE  1.00000000 0.50000000
USARGNP   0.50000000 1.00000000
Mean      1.00000000 1.00000000

estimate

Dependent Variable USAPRICE - Estimation by Mixed Estimation
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom   101
Centered R**2     0.999907      R Bar **2   0.999907
Uncentered R**2   0.999984      T x R**2     101.998
Mean of Dependent Variable      53.205882353
Std Error of Dependent Variable 24.065162461
Standard Error of Estimate       0.231678752
Sum of Squared Residuals        5.4211794375
Durbin-Watson Statistic             2.032795

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  USAPRICE{1}               1.558718576  0.063276664     24.63339
0.00000000
2.  USAPRICE{2}              -0.564449553  0.062927823     -8.96979
0.00000000
3.  USARGNP{1}                0.000036688  0.000490931      0.07473
0.94057554
4.  USARGNP{2}                0.000506875  0.000501614      1.01049
0.31467619
5.  Constant                 -0.796232629  0.201750915     -3.94661
0.00014664

F-Tests, Dependent Variable USAPRICE
Variable            F-Statistic       Signif
USAPRICE              68851.8400     0.0000000
USARGNP                   8.8141     0.0002963


Dependent Variable USARGNP - Estimation by Mixed Estimation
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom   101
Centered R**2     0.997654      R Bar **2   0.997654
Uncentered R**2   0.999903      T x R**2     101.990
Mean of Dependent Variable      2639.7245098
Std Error of Dependent Variable  551.4344454
Standard Error of Estimate        26.7063979
Sum of Squared Residuals        72036.400834
Durbin-Watson Statistic             1.949370

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  USAPRICE{1}               -8.52617351   5.78265018     -1.47444
0.14347331
2.  USAPRICE{2}                8.88189778   5.75035220      1.54458
0.12557472
3.  USARGNP{1}                 1.16968123   0.07879125     14.84532
0.00000000
4.  USARGNP{2}                -0.17729213   0.07989428     -2.21908
0.02871856
5.  Constant                  23.73450138  22.32510528      1.06313
0.29025804

F-Tests, Dependent Variable USARGNP
Variable            F-Statistic       Signif
USAPRICE                  2.0012     0.1404944
USARGNP                2486.7562     0.0000000


* Mixed regression by hand

* Compute S1, the standard error of auto regression on equation 1
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USAPRICE
LINREG(CMOMENT) USAPRICE
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}

Dependent Variable USAPRICE - Estimation by Least Squares
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom    97
Centered R**2     0.999911      R Bar **2   0.999907
Uncentered R**2   0.999985      T x R**2     101.998
Mean of Dependent Variable      53.205882353
Std Error of Dependent Variable 24.065162461
Standard Error of Estimate       0.231605150
Sum of Squared Residuals        5.2031717209
Regression F(4,97)               272586.2337
Significance Level of F           0.00000000
Durbin-Watson Statistic             2.463235
Q(25-0)                            25.940142
Significance Level of Q           0.41079860

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  Constant                 -0.584689219  0.209530831     -2.79047
0.00633768
2.  USAPRICE{1}               1.702187514  0.073717462     23.09070
0.00000000
3.  USAPRICE{2}              -0.707202173  0.073306405     -9.64721
0.00000000
4.  USARGNP{1}                0.000080177  0.000845945      0.09478
0.92468698
5.  USARGNP{2}                0.000328262  0.000869452      0.37755
0.70658905


* Two alternative ways to calculate S1, one with Degree of Freedom T-K,
the other T-NDET
COMPUTE S1=SQRT(%SEESQ)
*COMPUTE TEST1=%RSS/(%NOBS-1)
*COMPUTE S1=SQRT(TEST1)
DISPLAY S1 %SEESQ
      0.23161       0.05364

* Compute S2, the standard error of auto regression on equation 2
CMOMENT
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2} USARGNP
LINREG(CMOMENT) USARGNP
# CONSTANT USAPRICE{1 TO 2} USARGNP{1 TO 2}

Dependent Variable USARGNP - Estimation by Least Squares
Quarterly Data From 60:03 To 85:04
Usable Observations    102      Degrees of Freedom    97
Centered R**2     0.997688      R Bar **2   0.997593
Uncentered R**2   0.999904      T x R**2     101.990
Mean of Dependent Variable      2639.7245098
Std Error of Dependent Variable  551.4344454
Standard Error of Estimate        27.0542379
Sum of Squared Residuals        70997.383388
Regression F(4,97)                10465.8241
Significance Level of F           0.00000000
Durbin-Watson Statistic             2.127956
Q(25-0)                            21.316421
Significance Level of Q           0.67483977

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  Constant                  11.62277727  24.47569471      0.47487
0.63594696
2.  USAPRICE{1}              -15.95218521   8.61107693     -1.85252
0.06699205
3.  USAPRICE{2}               16.26287458   8.56306055      1.89919
0.06051095
4.  USARGNP{1}                 1.22350624   0.09881640     12.38161
0.00000000
5.  USARGNP{2}                -0.22393299   0.10156234     -2.20488
0.02982563

COMPUTE S2=SQRT(%SEESQ)
*COMPUTE TEST2=%RSS/(%NOBS-1)
*COMPUTE S2=SQRT(TEST2)
DISPLAY S2 %SEESQ
     27.05424     731.93179

* Compute the prior information for mixed regression

COMPUTE [RECTANGULAR] R =
||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||

COMPUTE [VECTOR] LITTLER = ||1,0,0,0,0||
COMPUTE [SYMMETRIC] V =
||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||
WRITE R LITTLER V
      1.0000         0.0000         0.0000         0.0000         0.0000

      0.0000         1.0000         0.0000         0.0000         0.0000

      0.0000         0.0000       233.6238         0.0000         0.0000

      0.0000         0.0000         0.0000       233.6238         0.0000

      0.0000         0.0000         0.0000         0.0000         0.0000



      1.0000         0.0000         0.0000         0.0000         0.0000



      0.0400
      0.0000         0.0400
      0.0000         0.0000         0.0400
      0.0000         0.0000         0.0000         0.0400
      0.0000         0.0000         0.0000         0.0000         0.0400




@mixed USAPRICE  1  60:1 85:4    R   LITTLER   V
# USAPRICE{1 TO 2} USARGNP{1 TO 2} CONSTANT
      0.96040

Dependent Variable USAPRICE - Estimation by Least Squares
Quarterly Data From 60:01 To 85:04
Usable Observations    102      Degrees of Freedom    97
 Total Observations    104      Skipped/Missing        2
Centered R**2     0.999908      R Bar **2   0.999904
Uncentered R**2   0.999984      T x R**2     101.998
Mean of Dependent Variable      53.205882353
Std Error of Dependent Variable 24.065162461
Standard Error of Estimate       0.235824529
Sum of Squared Residuals        5.3944812376
Regression F(4,97)               262918.3940
Significance Level of F           0.00000000
Durbin-Watson Statistic             2.062554
Q(26-0)                            32.607800
Significance Level of Q           0.17378298

   Variable                     Coeff       Std Error      T-Stat
Signif
*******************************************************************************

1.  USAPRICE{1}               1.567767815  0.064966164     24.13207
0.00000000
2.  USAPRICE{2}              -0.573452845  0.064607630     -8.87593
0.00000000
3.  USARGNP{1}                0.000038387  0.000506590      0.07577
0.93975458
4.  USARGNP{2}                0.000496622  0.000517796      0.95911
0.33988919
5.  Constant                 -0.782826295  0.205787277     -3.80406
0.00024902

--------------E444FCC7106BBD4BFD6B362A
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Content-Transfer-Encoding: 7bit

<!doctype html public "-//w3c//dtd html 4.0 transitional//en">
<html>
<b>Hi:</b>
<p><b>&nbsp;&nbsp;&nbsp; I am a user of WINRATS 4.3. Lately I have been
trying to reproduce the result of</b>
<br><b>Bayesian VAR (with Minnesota prior) through a Mixed Regression program.
I am able</b>
<br><b>to get really close resemblance in the coefficients, however, they
are not identical. In</b>
<br><b>what follows, please find my program code and output. My main questions
are:</b>
<br><b>1) Does built-in BVAR procedure first demean variables?</b>
<br><b>2) If not, how to handle deterministic variables? Is my way correct?</b>
<br><b>3) What is the reason for close, however not identical, regression
coefficients?</b>
<p><b>&nbsp;&nbsp;&nbsp; I look forward to your response. Thank you very
much.</b>
<br><b>Allison</b>
<p><b>A) Code for mixreg.src ( identical to the example you give on page
5-13 of manual</b>
<br><b>version 4, except that I adjust the degree of freedom from T-K to
T-NDET with NDET</b>
<br><b>being number of deterministic variables)</b>
<p><font face="Courier New,Courier"><font size=-1>PROCEDURE MIXED DEPVAR
NDET NBEG NEND CAPR LOWR V</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; SERIES&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; REAL&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
NDET</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; INTEGER&nbsp;&nbsp;&nbsp;&nbsp;
NBEG&nbsp; NEND ; * Estimation Range</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; RECTANGULAR
CAPR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ; * R matrix: m x NREG</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; VECTOR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
LOWR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ; * r vector: m x 1</font></font>
<br><font face="Courier New,Courier"><font size=-1>TYPE&nbsp; SYMMETRIC&nbsp;&nbsp;
V&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ; * V matrix: m
x m</font></font>
<br><font face="Courier New,Courier"><font size=-1>*</font></font>
<br><font face="Courier New,Courier"><font size=-1>LOCAL SYMMETRIC&nbsp;&nbsp;
XXMIXED</font></font>
<br><font face="Courier New,Courier"><font size=-1>LOCAL VECTOR&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
XYMIXED</font></font>
<br><font face="Courier New,Courier"><font size=-1>LOCAL INDEX&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
REGSUPP&nbsp;&nbsp;&nbsp; ; * Array for supplementary card</font></font>
<br><font face="Courier New,Courier"><font size=-1>*</font></font>
<br><font face="Courier New,Courier"><font size=-1>ENTER(VARYING) REGSUPP&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
; * Bring in supplementary card</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT NBEG NEND&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
; * CMOM including depvar</font></font>
<br><font face="Courier New,Courier"><font size=-1># REGSUPP DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOM, NOPRINT)
DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1># REGSUPP</font></font>
<br><font face="Courier New,Courier"><font size=-1>OVERLAY&nbsp; %CMOM(1,1)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
WITH XXMIXED(%NREG,%NREG)</font></font>
<br><font face="Courier New,Courier"><font size=-1>OVERLAY&nbsp; %CMOM(%NREG+1,1)
WITH XYMIXED(%NREG)</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE ADJ=(%NOBS-%NREG)/(%NOBS-NDET)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY ADJ</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE XXMIXED=XXMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*CAPR)</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE XYMIXED=XYMIXED+ADJ*%SEESQ*TR(CAPR)*(INV(V)*LOWR)</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOM) DEPVAR</font></font>
<br><font face="Courier New,Courier"><font size=-1>#REGSUPP</font></font>
<br><font face="Courier New,Courier"><font size=-1>END</font></font>
<br>&nbsp;
<br>&nbsp;
<p><b>B) Program code for doing mixed estimation regression.</b>
<p><font face="Courier New,Courier"><font size=-1>source(noecho) I:\winrats\uhero\mixreg.src</font></font>
<br><font face="Courier New,Courier"><font size=-1>cal 60 1 4</font></font>
<br><font face="Courier New,Courier"><font size=-1>allocate 85:4</font></font>
<br><font face="Courier New,Courier"><font size=-1>open data I:\winrats\usadata.rat</font></font>
<br><font face="Courier New,Courier"><font size=-1>data(format=rats) /</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Using built-in procedure
to do BVAR regression with Minnesota priors</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE GAMMA=0.2</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE FIJ=0.5</font></font>
<br><font face="Courier New,Courier"><font size=-1>system 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>variables usaprice usargnp</font></font>
<br><font face="Courier New,Courier"><font size=-1>lags 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>det constant</font></font>
<br><font face="Courier New,Courier"><font size=-1>specify(type=symmetric,tight=GAMMA)&nbsp;
FIJ</font></font>
<br><font face="Courier New,Courier"><font size=-1>end(system)</font></font>
<br><font face="Courier New,Courier"><font size=-1>estimate</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Mixed regression by
hand</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S1, the standard
error of auto regression on equation 1</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Two alternative ways
to calculate S1, one with Degree of Freedom T-K,</font></font>
<br><font face="Courier New,Courier"><font size=-1>the other T-NDET</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE S1=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST1=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S1=SQRT(TEST1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S1 %SEESQ</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S2, the standard
error of auto regression on equation 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE S2=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST2=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S2=SQRT(TEST2)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S2 %SEESQ</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute the prior information
for mixed regression</font></font>
<p><font face="Courier New,Courier"><font size=-1>COMPUTE [RECTANGULAR]
R =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [VECTOR] LITTLER
= ||1,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [SYMMETRIC]
V =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||</font></font>
<br><font face="Courier New,Courier"><font size=-1>WRITE R LITTLER V</font></font>
<p><font face="Courier New,Courier"><font size=-1>@mixed USAPRICE&nbsp;
1&nbsp; 60:1 85:4&nbsp;&nbsp;&nbsp; R&nbsp;&nbsp; LITTLER&nbsp;&nbsp; V</font></font>
<br><font face="Courier New,Courier"><font size=-1># USAPRICE{1 TO 2} USARGNP{1
TO 2} CONSTANT</font></font>
<br>&nbsp;
<br>&nbsp;
<br>&nbsp;
<p><b>C) Output.</b>
<br><font face="Courier New,Courier"><font size=-1>source(noecho) I:\winrats\uhero\mixreg.src</font></font>
<br><font face="Courier New,Courier"><font size=-1>cal 60 1 4</font></font>
<br><font face="Courier New,Courier"><font size=-1>allocate 85:4</font></font>
<br><font face="Courier New,Courier"><font size=-1>open data I:\winrats\usadata.rat</font></font>
<br><font face="Courier New,Courier"><font size=-1>data(format=rats) /</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Using built-in procedure
to do BVAR regression with Minnesota priors</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE GAMMA=0.2</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE FIJ=0.5</font></font>
<br><font face="Courier New,Courier"><font size=-1>system 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>variables usaprice usargnp</font></font>
<br><font face="Courier New,Courier"><font size=-1>lags 1 to 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>det constant</font></font>
<br><font face="Courier New,Courier"><font size=-1>specify(type=symmetric,tight=GAMMA)&nbsp;
FIJ</font></font>
<br><font face="Courier New,Courier"><font size=-1>end(system)</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>Summary of the Prior...</font></font>
<br><font face="Courier New,Courier"><font size=-1>Tightness Parameter
0.200000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Harmonic Lag Decay with
Parameter 0.000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Deviations
as Fraction of Tightness and Prior Means</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp; Listed Under
the Dependent Variable</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
USAPRICE&nbsp;&nbsp;&nbsp; USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>USAPRICE&nbsp; 1.00000000
0.50000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>USARGNP&nbsp;&nbsp;
0.50000000 1.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.00000000 1.00000000</font></font>
<p><font face="Courier New,Courier"><font size=-1>estimate</font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USAPRICE
- Estimation by Mixed Estimation</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp; 101</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.999907&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.999907</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999984&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.998</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
53.205882353</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable 24.065162461</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.231678752</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.4211794375</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.032795</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.558718576&nbsp; 0.063276664&nbsp;&nbsp;&nbsp;&nbsp; 24.63339</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.564449553&nbsp; 0.062927823&nbsp;&nbsp;&nbsp;&nbsp; -8.96979</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000036688&nbsp; 0.000490931&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.07473</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.94057554</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000506875&nbsp; 0.000501614&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.01049</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.31467619</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.796232629&nbsp; 0.201750915&nbsp;&nbsp;&nbsp;&nbsp; -3.94661</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00014664</font></font>
<p><font face="Courier New,Courier"><font size=-1>F-Tests, Dependent Variable
USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1>Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
F-Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>USAPRICE&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
68851.8400&nbsp;&nbsp;&nbsp;&nbsp; 0.0000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>USARGNP&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
8.8141&nbsp;&nbsp;&nbsp;&nbsp; 0.0002963</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USARGNP
- Estimation by Mixed Estimation</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp; 101</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.997654&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.997654</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999903&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.990</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2639.7245098</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable&nbsp; 551.4344454</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
26.7063979</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
72036.400834</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.949370</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-8.52617351&nbsp;&nbsp; 5.78265018&nbsp;&nbsp;&nbsp;&nbsp; -1.47444</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.14347331</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
8.88189778&nbsp;&nbsp; 5.75035220&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.54458</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.12557472</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.16968123&nbsp;&nbsp; 0.07879125&nbsp;&nbsp;&nbsp;&nbsp; 14.84532</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.17729213&nbsp;&nbsp; 0.07989428&nbsp;&nbsp;&nbsp;&nbsp; -2.21908</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.02871856</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
23.73450138&nbsp; 22.32510528&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.06313</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.29025804</font></font>
<p><font face="Courier New,Courier"><font size=-1>F-Tests, Dependent Variable
USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
F-Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>USAPRICE&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.0012&nbsp;&nbsp;&nbsp;&nbsp; 0.1404944</font></font>
<br><font face="Courier New,Courier"><font size=-1>USARGNP&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2486.7562&nbsp;&nbsp;&nbsp;&nbsp; 0.0000000</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>* Mixed regression by
hand</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S1, the standard
error of auto regression on equation 1</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USAPRICE</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USAPRICE
- Estimation by Least Squares</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp;&nbsp;
97</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.999911&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.999907</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999985&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.998</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
53.205882353</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable 24.065162461</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.231605150</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.2031717209</font></font>
<br><font face="Courier New,Courier"><font size=-1>Regression F(4,97)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
272586.2337</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
F&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.463235</font></font>
<br><font face="Courier New,Courier"><font size=-1>Q(25-0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
25.940142</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
Q&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.41079860</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.584689219&nbsp; 0.209530831&nbsp;&nbsp;&nbsp;&nbsp; -2.79047</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00633768</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.702187514&nbsp; 0.073717462&nbsp;&nbsp;&nbsp;&nbsp; 23.09070</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.707202173&nbsp; 0.073306405&nbsp;&nbsp;&nbsp;&nbsp; -9.64721</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000080177&nbsp; 0.000845945&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.09478</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.92468698</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000328262&nbsp; 0.000869452&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.37755</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.70658905</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>* Two alternative ways
to calculate S1, one with Degree of Freedom T-K,</font></font>
<br><font face="Courier New,Courier"><font size=-1>the other T-NDET</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE S1=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST1=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S1=SQRT(TEST1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S1 %SEESQ</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.23161&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.05364</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute S2, the standard
error of auto regression on equation 2</font></font>
<br><font face="Courier New,Courier"><font size=-1>CMOMENT</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2} USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1>LINREG(CMOMENT) USARGNP</font></font>
<br><font face="Courier New,Courier"><font size=-1># CONSTANT USAPRICE{1
TO 2} USARGNP{1 TO 2}</font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USARGNP
- Estimation by Least Squares</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:03 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp;&nbsp;
97</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.997688&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.997593</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999904&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.990</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2639.7245098</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable&nbsp; 551.4344454</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
27.0542379</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
70997.383388</font></font>
<br><font face="Courier New,Courier"><font size=-1>Regression F(4,97)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
10465.8241</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
F&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.127956</font></font>
<br><font face="Courier New,Courier"><font size=-1>Q(25-0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
21.316421</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
Q&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.67483977</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat</font></font>
<br><font face="Courier New,Courier"><font size=-1>Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
11.62277727&nbsp; 24.47569471&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.47487</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.63594696</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-15.95218521&nbsp;&nbsp; 8.61107693&nbsp;&nbsp;&nbsp;&nbsp; -1.85252</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.06699205</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
16.26287458&nbsp;&nbsp; 8.56306055&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.89919</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.06051095</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.22350624&nbsp;&nbsp; 0.09881640&nbsp;&nbsp;&nbsp;&nbsp; 12.38161</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.22393299&nbsp;&nbsp; 0.10156234&nbsp;&nbsp;&nbsp;&nbsp; -2.20488</font></font>
<br><font face="Courier New,Courier"><font size=-1>0.02982563</font></font>
<p><font face="Courier New,Courier"><font size=-1>COMPUTE S2=SQRT(%SEESQ)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE TEST2=%RSS/(%NOBS-1)</font></font>
<br><font face="Courier New,Courier"><font size=-1>*COMPUTE S2=SQRT(TEST2)</font></font>
<br><font face="Courier New,Courier"><font size=-1>DISPLAY S2 %SEESQ</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;
27.05424&nbsp;&nbsp;&nbsp;&nbsp; 731.93179</font></font>
<p><font face="Courier New,Courier"><font size=-1>* Compute the prior information
for mixed regression</font></font>
<p><font face="Courier New,Courier"><font size=-1>COMPUTE [RECTANGULAR]
R =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||1,0,0,0,0|0,1,0,0,0|0,0,S2/(S1*FIJ),0,0|0,0,0,S2/(S1*FIJ),0|0,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [VECTOR] LITTLER
= ||1,0,0,0,0||</font></font>
<br><font face="Courier New,Courier"><font size=-1>COMPUTE [SYMMETRIC]
V =</font></font>
<br><font face="Courier New,Courier"><font size=-1>||GAMMA**2|0,GAMMA**2|0,0,GAMMA**2|0,0,0,GAMMA**2|0,0,0,0,GAMMA**2||</font></font>
<br><font face="Courier New,Courier"><font size=-1>WRITE R LITTLER V</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 1.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
233.6238&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 233.6238&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000</font></font>
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0400</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.0000&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.0400</font></font>
<br>&nbsp;
<br>&nbsp;
<p><font face="Courier New,Courier"><font size=-1>@mixed USAPRICE&nbsp;
1&nbsp; 60:1 85:4&nbsp;&nbsp;&nbsp; R&nbsp;&nbsp; LITTLER&nbsp;&nbsp; V</font></font>
<br><font face="Courier New,Courier"><font size=-1># USAPRICE{1 TO 2} USARGNP{1
TO 2} CONSTANT</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.96040</font></font>
<p><font face="Courier New,Courier"><font size=-1>Dependent Variable USAPRICE
- Estimation by Least Squares</font></font>
<br><font face="Courier New,Courier"><font size=-1>Quarterly Data From
60:01 To 85:04</font></font>
<br><font face="Courier New,Courier"><font size=-1>Usable Observations&nbsp;&nbsp;&nbsp;
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Degrees of Freedom&nbsp;&nbsp;&nbsp;
97</font></font>
<br><font face="Courier New,Courier"><font size=-1>&nbsp;Total Observations&nbsp;&nbsp;&nbsp;
104&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Skipped/Missing&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2</font></font>
<br><font face="Courier New,Courier"><font size=-1>Centered R**2&nbsp;&nbsp;&nbsp;&nbsp;
0.999908&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; R Bar **2&nbsp;&nbsp; 0.999904</font></font>
<br><font face="Courier New,Courier"><font size=-1>Uncentered R**2&nbsp;&nbsp;
0.999984&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; T x R**2&nbsp;&nbsp;&nbsp;&nbsp;
101.998</font></font>
<br><font face="Courier New,Courier"><font size=-1>Mean of Dependent Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
53.205882353</font></font>
<br><font face="Courier New,Courier"><font size=-1>Std Error of Dependent
Variable 24.065162461</font></font>
<br><font face="Courier New,Courier"><font size=-1>Standard Error of Estimate&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.235824529</font></font>
<br><font face="Courier New,Courier"><font size=-1>Sum of Squared Residuals&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
5.3944812376</font></font>
<br><font face="Courier New,Courier"><font size=-1>Regression F(4,97)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
262918.3940</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
F&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>Durbin-Watson Statistic&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
2.062554</font></font>
<br><font face="Courier New,Courier"><font size=-1>Q(26-0)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
32.607800</font></font>
<br><font face="Courier New,Courier"><font size=-1>Significance Level of
Q&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.17378298</font></font>
<p><font face="Courier New,Courier"><font size=-1>&nbsp;&nbsp; Variable&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
Coeff&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Std Error&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
T-Stat&nbsp;&nbsp;&nbsp; Signif</font></font>
<br><font face="Courier New,Courier"><font size=-1>*******************************************************************************</font></font>
<p><font face="Courier New,Courier"><font size=-1>1.&nbsp; USAPRICE{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1.567767815&nbsp; 0.064966164&nbsp;&nbsp;&nbsp;&nbsp; 24.13207 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>2.&nbsp; USAPRICE{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.573452845&nbsp; 0.064607630&nbsp;&nbsp;&nbsp;&nbsp; -8.87593 0.00000000</font></font>
<br><font face="Courier New,Courier"><font size=-1>3.&nbsp; USARGNP{1}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000038387&nbsp; 0.000506590&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.07577 0.93975458</font></font>
<br><font face="Courier New,Courier"><font size=-1>4.&nbsp; USARGNP{2}&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
0.000496622&nbsp; 0.000517796&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 0.95911 0.33988919</font></font>
<br><font face="Courier New,Courier"><font size=-1>5.&nbsp; Constant&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
-0.782826295&nbsp; 0.205787277&nbsp;&nbsp;&nbsp;&nbsp; -3.80406 0.00024902</font></font></html>

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--------------9090E4371E79398487DF3633--


---------- End of message ----------

From: Rob Trevor <robt@mafc.mq.edu.au>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: [Fwd: question about BVAR]
Date: Wed, 21 Jun 2000 17:35:05 +1000
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Allison

Posting your message to the list 3 times in 5 hours is more likely to 
ensure that you do NOT get an answer to your question.

If someone is interested in what you are trying to do, they will 
eventually try to help. If you are in urgent need of help, PHONE 
Estima's tech support line (see their web site).

Rob

---------- End of message ----------

From: Yuen Phui Ling Hazel <fbap8383@nus.edu.sg>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Matrix Multiplication
Date: Wed, 21 Jun 2000 15:49:04 +0800
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Hello everyone, 

Does someone know the syntax to matrix multiplication? 

Thanks in advance. 

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From: =?iso-8859-1?q?slim=20skandes?= <slim_skander@yahoo.fr>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: modified R/S
Date: Wed, 21 Jun 2000 11:47:45 +0200 (CEST)
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Hello=20
I m a student in PARIS X university (France).I m
preparing a working paper dealing with the presence of
long memory in finantial markets.
I have programs computing the hurst exponent by the
rescaled range method and the GPH method (Geweke
Porter-Hudak). I want to apply the modified rescaled
range method proposed by A.Lo (1991).
AS i m beggining with RATS i couldn't do the progam .
can you send me the program (for RATS ) computing the
hurst exponent with the modified rescaled range method
or tell me where can i find them.
please help me i can't find it anywhere.

thank you





___________________________________________________________
Do You Yahoo!?
Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr

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From: virginie traclet <vtraclet@univ-rennes1.fr>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: kolmogorov-smirnov statistics
Date: Wed, 21 Jun 2000 14:51:11 +0200
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Dear RATS users,

Do you know if the Kolmogorov-Smirnov statistics, which is necessary to
compute the interval for the CUSUM=B2 test, is in RATS ? I have looked for
this in the RATS manual and in the RATS help but haven't found it . If you
have some insights about this subject .

Thanks for your help

Virginie

***********************************************
Virginie Traclet
Universit=E9 de Rennes 1
France
e-mail : virginie.traclet@univ-rennes1.fr
***********************************************



---------- End of message ----------

From: cfb <baum@bc.edu>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Matrix Multiplication
Date: Wed, 21 Jun 2000 09:20:55 -0400
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I think you will find it quite easily if you Read The Fine Manual.

Kit Baum

--On Wednesday, June 21, 2000 3:49 PM +0800 Yuen Phui Ling Hazel 
<fbap8383@nus.edu.sg> wrote:

>
> Hello everyone,
>
> Does someone know the syntax to matrix multiplication?
>
> Thanks in advance.





---------- End of message ----------

From: "Sergio Zuniga" <szuniga@socompa.ucn.cl>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: RE: Matrix Multiplication
Date: Wed, 21 Jun 2000 10:22:23 -0600
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KioqKioqKioqKioqKg0K


---------- End of message ----------

From: "Estima" <tomm@estima.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: question about BVAR
Date: Wed, 21 Jun 2000 15:32:22 -0500
Errors-to: <rats-l-owner@efs.mq.edu.au>
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On 20 Jun 00, at 12:51, Allison wrote:

> Dear Staff:
> 
>     I am a user of WINRATS 4.3. Lately I have been trying to reproduce
> the result of Bayesian VAR (with Minnesota prior) through a Mixed
> Regression program. 

Allison:

I've cc'd the RATS mailing list on this message because I think it 
applies there as well. Please send any responses intended directly 
for Estima to estima@estima.com, not to the list address.

First, in order for us to provide support, I need you to send include 
your name and your RATS serial number so we know who you are.

Second, As a reminder to you and everyone else on the RATS list, 
please don't send queries both to Estima _and_ to the RATS mailing 
list. If both we at Estima and some other helpful "private citizens" 
on the mailing list are spending time trying to come up with an 
answer your query, then someone is wasting time they could be 
spending on other things. So, one target at a time please.

Thanks,
Tom Maycock
Estima



--
------------------------------------------------------------
|   Estima                    |  Sales:   (800) 822-8038   |
|   P.O. Box 1818             |           (847) 864-8772   |
|   Evanston, IL 60204-1818   |  Support: (847) 864-1910   |
|   USA                       |  Fax:     (847) 864-6221   |
|   http://www.estima.com     |  estima@estima.com         |
------------------------------------------------------------

---------- End of message ----------

From: "Estima" <tomm@estima.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Matrix Multiplication
Date: Wed, 21 Jun 2000 15:38:52 -0500
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On 21 Jun 00, at 9:20, cfb wrote:

> I think you will find it quite easily if you Read The Fine Manual.
> 
> Kit Baum
> 

My thoughs exactly. The RATS manual isn't perfect, but I'm pretty 
sure it covers matrix multiplication. 

In the midst of many hours spent working on the v. 5 manual, with the 
end nearly in sight, sometimes I just have to wonder why we even 
bother....

Tom Maycock
Estima

--
------------------------------------------------------------
|   Estima                    |  Sales:   (800) 822-8038   |
|   P.O. Box 1818             |           (847) 864-8772   |
|   Evanston, IL 60204-1818   |  Support: (847) 864-1910   |
|   USA                       |  Fax:     (847) 864-6221   |
|   http://www.estima.com     |  estima@estima.com         |
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---------- End of message ----------

From: Rob Trevor <robt@mafc.mq.edu.au>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Matrix Multiplication
Date: Thu, 22 Jun 2000 07:34:39 +1000
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Tom

At 3:38 PM -0500 21/6/00, Estima wrote:
>...
>In the midst of many hours spent working on the v. 5 manual, with the
>end nearly in sight, sometimes I just have to wonder why we even
>bother....

It IS extremely useful to those of us who have legit copies :)

Mind you, I've always figured that those who don't have their manual 
readily available (it is a bit inconvenient to carry everywhere) and 
can't figure how to use the online help or look through some of the 
provided examples and procedures, shouldn't be allowed to use a 
computer, let alone something as powerful as RATS :)

Looking forward to V5...

Rob

---------- End of message ----------

From: Yuen Phui Ling Hazel <fbap8383@nus.edu.sg>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: RE: Matrix Multiplication
Date: Thu, 22 Jun 2000 10:34:21 +0800
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Thanks Sergio and everyone for your kind replies. 

Warm Rgds. 

 -----Original Message-----
From: 	Sergio Zuniga [mailto:szuniga@socompa.ucn.cl] 
Sent:	Thursday, June 22, 2000 12:22 AM
To:	RATS Discussion List
Subject:	RE: Matrix Multiplication

> Hello everyone, 
> 
> Does someone know the syntax to matrix multiplication? 
> 
> Thanks in advance.


dec rect X Y
comp Y = ||100|106|107|120|110|116|123|133|137||
comp X =
||1,100,100|1,104,99|1,106,110|1,111,126|1,111,113|1,115,103|1,120,102|$
 1,124,103|1,126,98||

com beta = inv(tr(X)*X)*(tr(X)*Y)
write beta
    -49.3413
      1.3642
      0.1139



Cheers,

***************************************************
Sergio Zuniga       szuniga@ucn.cl             
Universidad Catolica del Norte  
Coquimbo - Chile - Tel.: (09)4199197                        
***************************************************

---------- End of message ----------

From: Klaus Fischer <Klaus.Fischer@fas.ulaval.ca>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Manual
Date: Thu, 22 Jun 2000 10:02:12 -0400
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Hi Tom:

> In the midst of many hours spent working on the v. 5 manual, with the
> end nearly in sight, sometimes I just have to wonder why we even
> bother....
>

Keep up the good work. The manual IS very much appreciated in its balance
of not too technical and not too dumb..... by some at least. And if it
gets improved, well that's equally appreciated!

Klaus Fischer



---------- End of message ----------

From: Simon.Van-Norden@hec.ca
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Manual
Date: Thu, 22 Jun 2000 10:58:13 -0400
Errors-to: <rats-l-owner@efs.mq.edu.au>
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I wanted to try to make some constructive suggestions regarding the manua=
l (if
its not too late already.) I agree with Klaus that RATS usually gets it r=
ight in
the balance between technical/dumb, the use of examples, etc. However, I'=
d wish
for two changes;

1) Consolidation; Some topics are just too fragmented. Part of the descri=
ption
might be in Chapter 1, some in Chapter 4, some in Chap. 14 and some in th=
e
appendices. Or it might be only one of these places, but I can't tell whi=
ch and
have to check them all. I think I'm wishing that Chap. 14 were more compl=
ete,
even if this meant more duplication of material found elsewhere.

2) Chapter 9: I've always had trouble wrapping my mind around RATS's feat=
ures
for defining, manipulating and solving equations (and systems of equation=
s.) It
leaves me wishing this chapter were not so terse.


Just my 2 cents.

SvN


Klaus Fischer wrote:
>=20
> Hi Tom:
>=20
> > In the midst of many hours spent working on the v. 5 manual, with the
> > end nearly in sight, sometimes I just have to wonder why we even
> > bother....
> >
>=20
> Keep up the good work. The manual IS very much appreciated in its balan=
ce
> of not too technical and not too dumb..... by some at least. And if it
> gets improved, well that's equally appreciated!
>=20
> Klaus Fischer

--=20
Simon van Norden, Prof. agr=E9g=E9, www.hec.ca/pages/simon.van-norden
Service de l'enseignement de la finance, =C9cole des H.E.C.
3000 Cote-Sainte-Catherine, Montreal QC, CANADA   H3T 2A7
simon.van-norden@hec.ca or (514)340-6781 or fax:(514)340-5632

---------- End of message ----------

From: Luca Cazzulani <luca.cazzulani@uni-bocconi.it>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: unsubscribe
Date: Thu, 22 Jun 2000 18:03:12 +0100
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unsubscribe


---------- End of message ----------

From: "Estima" <tomm@estima.com>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: Manual
Date: Thu, 22 Jun 2000 11:06:11 -0500
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> I wanted to try to make some constructive suggestions regarding the manual (if
> its not too late already.) I agree with Klaus that RATS usually gets it right in
> the balance between technical/dumb, the use of examples, etc. However, I'd wish
> for two changes;

We always appreciate constructive criticism! It is close to being too 
late, but we are still finalizing some things. I think we've already 
addressed some of your ideas though. 
> 
> 1) Consolidation; Some topics are just too fragmented. Part of the description
> might be in Chapter 1, some in Chapter 4, some in Chap. 14 and some in the
> appendices. Or it might be only one of these places, but I can't tell which and
> have to check them all. I think I'm wishing that Chap. 14 were more complete,
> even if this meant more duplication of material found elsewhere.

I think you'll find Version 5 to improve on this. 

First, we've split into two books, using a smaller 7x9 format. This 
is primarily in response to people who wanted to have the "reference" 
section (Chapters 14 and 15 of current edition) in a more portable 
format, and because the manual would just have gotten too big and 
unwieldy otherwise.

I don't know if you'll find that the reference section is more 
complete (although it does document functions much more extensively), 
and it some ways it may even be a bit more brief. However, I think 
we've gotten more consistent about where information appears (i.e. in 
the User's Guide section vs. the Reference section), and we are 
_much_ more consistent about providing technical details/algorithm 
info, etc.

Chapter 1 has been expanded somewhat, with a revised and expanded 
tutorial example, and covering things like functions, computations, 
and procedures in a bit more detail. I think it makes for a more 
complete introduction to the program. 

Chapter 4 has been split into two parts--one chapter on scalar/matrix 
manipulations, data types, etc., which most people will want to know, 
and a separate "programmer's" chapter with details on writing 
procedures, repetitive analysis routines, interactive programs, and 
the like--which only interest a portion of the user base.

> 2) Chapter 9: I've always had trouble wrapping my mind around RATS's features
> for defining, manipulating and solving equations (and systems of equations.) It
> leaves me wishing this chapter were not so terse.

The chapter 9 (now Chapter 11) contents haven't really changed all 
that much, but, due to significant changes to the program itself, an 
expanded example, and more technical details, I think you'll be happy 
with the changes.

For example, a big change in RATS 5 is that you can now create MODELS 
that contain linear equations, non-linear equations, or a mix of both-
-previously MODELS could only contain non-linear FRMLS, so "models" 
of equations required repeating long lists of supplementary cards. It 
is also much easier to define a MODEL, and you can even combine 
MODELS into a bigger MODEL. This, along with improved options for 
saving results, makes handling VAR analysis, multivariate 
forecasting, etc., much easier.

OK, that's enough hints for now. I'll save details on constrained 
optimization, "parameter sets", new instructions, new functions, etc. 
for later!

No, I don't know when it will ship yet, so please don't ask. But, we 
should be posting details on new features fairly soon on the web 
site, along with an expected release date (newsletter to follow). And 
we always need more beta testers!

Thanks,
Tom Maycock
Estima


--
------------------------------------------------------------
|   Estima                    |  Sales:   (800) 822-8038   |
|   P.O. Box 1818             |           (847) 864-8772   |
|   Evanston, IL 60204-1818   |  Support: (847) 864-1910   |
|   USA                       |  Fax:     (847) 864-6221   |
|   http://www.estima.com     |  estima@estima.com         |
------------------------------------------------------------

---------- End of message ----------

From: gkoutmos@FAIR1.FAIRFIELD.EDU
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From: =?iso-8859-1?q?slim=20skandes?= <slim_skander@yahoo.fr>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: modified R/S
Date: Fri, 23 Jun 2000 13:00:31 +0200 (CEST)
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Hello=20
I m a student in PARIS X university (France).I m
preparing a working paper dealing with the presence of
long memory in finantial markets.
I have programs computing the hurst exponent by the
rescaled range method and the GPH method (Geweke
Porter-Hudak). I want to apply the modified rescaled
range method proposed by A.Lo (1991).
AS i m beggining with RATS i couldn't do the progam .
can you send me the program (for RATS ) computing the
hurst exponent with the modified rescaled range method
or tell me where can i find them.
please help me i can't find it anywhere.

thank you






___________________________________________________________
Do You Yahoo!?
Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr

---------- End of message ----------

From: =?iso-8859-1?q?slim=20skandes?= <slim_skander@yahoo.fr>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: run test
Date: Mon, 26 Jun 2000 17:08:54 +0200 (CEST)
Errors-to: <rats-l-owner@efs.mq.edu.au>
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does someone has the code for a run test (non
parametric test of serial correlation)
thank you






___________________________________________________________
Do You Yahoo!?
Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr

---------- End of message ----------

From: Binelli Maurizio <mbinelli@FIDEURAMCAPITAL.IT>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Quantile regression
Date: Wed, 28 Jun 2000 16:07:42 +0200
Errors-to: <rats-l-owner@efs.mq.edu.au>
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Dear RATS users,

	I got in trouble using the little flexible quantile regression
procedure RQ. Does someone have one more flexible?


	Many thanks in advance.

Maurizio.




---------- End of message ----------

From: baum <baum@bc.edu>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Re: modified R/S
Date: Thu, 29 Jun 2000 08:48:59 -0400
Errors-to: <rats-l-owner@efs.mq.edu.au>
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Code to calculate the Lo modified R/S test (and, as a special case, the 
classical Hurst-Mandelbrot R/S test) is available at

http://ideas.uqam.ca/ideas/data/Softwares/bocbocodeS412601.html

This is written in Stata, but it should be fairly straightforward to 
translate to RATS, especially since RATS has the MCOV facility to do the 
Newey-West piece more succinctly than it may be done in Stata. The code is 
reasonably well documented and comes with a help file explaining how it 
works. The data may be accessed over the Internet, since Stata can open a 
dataset from a URL.

Please note that the SSC-IDEAS archive is open to contributions of 
well-documented code for all major packages, and contains RATS, MATLAB, Ox, =

and Mathematica modules as well as (predominantly) Stata among its 483 
components. The predominance of Stata modules reflects the heavy traffic 
among StataList users, and the manner in which Stata modules may be 
installed to appear as native commands, extending the language accordingly.

Kit Baum
Boston College Economics
SSC-IDEAS maintainer
http://ideas.uqam.ca/ideas/data/bocbocode.html


--On Friday, June 23, 2000 13.00 +0200 slim skandes <slim_skander@yahoo.fr> =

wrote:

> Hello
> I m a student in PARIS X university (France).I m
> preparing a working paper dealing with the presence of
> long memory in finantial markets.
> I have programs computing the hurst exponent by the
> rescaled range method and the GPH method (Geweke
> Porter-Hudak). I want to apply the modified rescaled
> range method proposed by A.Lo (1991).
> AS i m beggining with RATS i couldn't do the progam .
> can you send me the program (for RATS ) computing the
> hurst exponent with the modified rescaled range method
> or tell me where can i find them.
> please help me i can't find it anywhere.
>
> thank you
>
>
>
>
>
>
> ___________________________________________________________
> Do You Yahoo!?
> Achetez, vendez! =C0 votre prix! Sur http://encheres.yahoo.fr



-----------------------------------------------------------------
Kit Baum    baum@bc.edu    http://fmwww.bc.edu/ec-v/baum.fac.html

---------- End of message ----------

From: virginie traclet <vtraclet@univ-rennes1.fr>
To: "RATS Discussion List" <RATS-L@efs.mq.edu.au>
Subject: Chow tests
Date: Fri, 30 Jun 2000 12:16:19 +0200
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Dear RATS users,

I want to make Chow tests without knowing the break date a priori, so I
make Chow test with all possible dates of my sample period ( see the
example of program below) : is it possible to do it ? 

*******************Chow test for the period 1970:1 1997:4 for a bivariate
VAR including 5 lags on nominal GDP and adjusted monetary base (both in
first differences of logarithms) **************

do time = 1972:1, 1997:4
	linreg dlpibn 1970:1 time
	#constant dlpibn{1 to 5} dlbasea{1 to 5}
	compute rss1=%rss

	linreg dlpibn time 1997:4
	#constant dlpibn{1 to 5} dlbasea{1 to 5}
	compute rss2=%rss

	linreg dlpibn 1970:1 1997:4
	#constant dlpibn{1 to 5} dlbasea{1 to 5}
	compute rsstotal=%rss
	compute nobstotal=%nobs

	compute F = ((rsstotal - rss1 - rss2) / %nreg ) / ((rss1 +
rss2)/(nobstotal - 2*%nreg))
	cdf ftest F %nreg nobstotal-2*%nreg

end do time
***************************************



Thanks for your help

Regards,

Virginie



---------- End of message ----------