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help for ^hegy4^          (Statalist distribution, 27 August 2001)
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Hylleberg-Engle-Granger-Yoo (HEGY) Seasonal unit root test for quarterly data
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  ^hegy4^ varname  [^if^ exp] [^in^ range] [, ^L^ags(numlist) 
                             ^D^et(none|const|seas|trend|strend|mult) 
				        ^GEN^erate(newvar) ^NOT^est ^LEV^el(integer)]


^hegy4^ is for use with quarterly time-series data.  You must ^tsset^ your data before 
using ^hegy4^; see help @tsset@.

^varname^ may contain time-series operators; see help @varlist@.


Description
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^hegy4^ performs the Hylleberg et al. (HEGY, 1990) test for seasonal unit roots
in a quarterly timeseries. It estimates the four roots of the timeseries
representation (1-B^^4) x(t) = e(t), where B is the backshift operator, and
presents estimates of these roots as Pi(1)..Pi(4). A joint test for Pi(3)=Pi(4)=0
is also presented. Critical values are those appropriate for T=100, taken from
HEGY Table 1. Joint tests for Pi(2)=Pi(3)=Pi(4)=0 and Pi(1)=Pi(2)=Pi(3)=Pi(4)=0,
with critical values, are those presented by Ghysels et al. (1994). Critical
values for the case of muliplicative seasonality (see below) are from tables 1a-c
in Smith and Taylor (1998). Critical values are linearly interpolated for sample
sizes in the ranges (48,100) and (100,200).


Options
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^Det^, which may take on values ^none^, ^const^, ^seas^, ^trend^, ^strend^ or ^mult^, specifies
the process to be tested. The default, as suggested by HEGY and Ghysels et al. (1994),
is ^seas^, indicating that a set of 3 seasonal dummies plus constant are to be
included in the regression. ^none^ specifies that no deterministic variables are
to be included; ^const^ specifies only a constant. ^trend^ specifies that a trend
is to be included along with a constant term. ^strend^ specifies that a trend is
to be included along with seasonal dummies and a constant term. ^mult^ specifies
that seasonal intercepts (the case of multiplicative seasonality, recommended
by Smith and Taylor (1998)) are to be included along with seasonal dummies and a
constant term.

^Lags(^numlist^)^ specifies the lag orders to be used in augmenting the model with
lags of the fourth difference of the timeseries. Its default is zero. If sequential
lags are specified starting with 1, HEGY4 automatically conducts a sequential t-test
to determine the optimal lag length and optimal lags to be included in the auxiliary
regression. The ^LEVel(^#^)^ option may be used to control the size of the lag length
test. Note that the test size equals 1 minus the confidence interval (in percent).
Taylor and Smith (2001, p. 204) recommend a test size of 25%, which corresponds to
^LEV(75)^ on the command line. The ^NOTest^ option may be specified to suppress the
lag length test and utilize the lags specified in the option in generating the test
statistic.

^GEN^erate(^newvar^): as a diagnostic on the procedure, the residuals from the HEGY
regression may themselves be regressed on four lags and the original regressors.
The residuals from that auxiliary regression may optionally be saved via the
^GEN^erate() option, which saves them as a new variable. Other diagnostic
procedures (such as a portmanteau test, e.g. ^wntestq^, or tests for normality,
skewness and kurtosis) may be then applied to this variable. 

Examples
--------

	. ^use http://fmwww.bc.edu/ec-p/data/Mills2d/exchq^

	. ^hegy4 exchq^
	
	. ^hegy4 exchq, det(strend) lag(1/4)^
	
	. ^hegy4 exchq, lag(1/4) level(75)^
	
	. ^hegy4 exchq, det(seas) lag(1 3 5)^
	
	. ^hegy4 exchq, det(mult) lag(1/8) notest^

	. ^hegy4 exchq, gen(hegyres)^
	. ^wntestq hegyres^


References
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Franses, P. H., and B. Hobijn. 1997. Critical Values for Unit Root Tests In 
Seasonal Time Series. Journal of Applied Statistics 24: 25-47.

Ghysels, E., Lee, H.S., and J. Noh. 1994. Testing for Unit Roots in Seasonal
Time Series: Some Theoretical Extensions and a Monte Carlo Investigation.
Journal of Econometrics, 62, 415-442.

Hylleberg, S., Engle, R.F., Granger, C.W.J. and B.S. Yoo. 1990. Seasonal
Integration and Cointegration. Journal of Econometrics, 44, 215-238.

Smith, R. J., and A. M. R. Taylor. 1998. Additional Critical Values and
Asymptotic Representations for Seasonal Unit Root Tests,
Journal of Econometrics, 85, 269-88.

Taylor, A. M. R., and R. J. Smith. 2001. Tests of the Seasonal Unit-Root
Hypothesis Against Heteroscedastic Seasonal Integration,
Journal of Business & Economic Statistics, 19, 192-207.

Acknowledgements
----------------

This routine is based on the HEGY.SRC RATS code written by Jean-Philip
Bellotteau and available from the SSC-IDEAS archive. We thank M. Bellotteau 
and P.H. Franses for clarifying remarks. Remaining errors are ours.

Authors
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Christopher F Baum, Boston College, USA
baum@@bc.edu

Richard Sperling, The Ohio State University, USA
rsperling@@boo.net

Also see
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Manual:  ^[R] dfuller^
On-line:  help for @dfuller@, @time@, @tsset@, @dfgls@ (if installed)
