Vector autoregression ---------------------
^vecar6^ depvarlist [^if^ exp] [^in^ range] ^,^ ^m^axlag^(^#^)^ [ ^noc^on > stant ^e^xog^(^varlist^)^ ^cov^ ^dfk^ ^noh^eader ^t^able ^l^evel^(^#^)^ > ^s^aving^(^name^)^ ^u^sing^(^name^)^ ^uncorr^ ]
^vecar6^ is for use with time-series data. You must ^tsset^ your data before using ^vecar6^; see help @tsset@.
^vecar6^ shares the features of all estimation commands; see help @est@.
The syntax of @predict@ following ^vecar6^ is
^predict^ [type] newvarname [^if^ exp] [^in^ range] ^,^ [ ^eq^uation^(^eqno > ^)^ { ^xb^ | ^stdp^ | ^r^esiduals | ^d^ifferences | ^stdd^ > p }
These statistics are available both in and out of sample; type ^predict^ ... ^if e(sample)^ ... if wanted only for the estimation sample.
Description -----------
^vecar6^ estimates vector autoregression (VAR) models. Each of the variables in depvarlist is regressed on ^maxlag(^#^)^ lags of depvarlist, a constant (unless suppressed) and the exogenous variables provided in varlist (if any). varlist may contain time-series operators.
A set of "block F" tests evaluates the joint significance of each variable's lagged values in each equation.
Options -------
^maxlag(^#^)^ must be specified, and must be at least 1.
^noconstant^ omits the constant term from estimation.
^exog(^varlist^)^ specifies the exogenous variables to be included in each equation.
^cov^ displays the covariance matrix of the residuals between equations. The divisor of the covariance terms is T, the number of sample observations, unless the dfk option is invoked. A comparison of this model with the zero-lag model (as a likelihood ratio test) is computed. Three criteria often employed for lag length selection are produced: the AIC (Akaike Information Criterion), BIC (Bayes or Schwarz Information Criterion) and the HQ (Hannan-Quinn) criterion. The cov option also causes three tests on the residuals to be performed: the multivariate portmanteau test of Ljung and Box, implemented in @wntstmvq@ (STB-60), the test for independence of the errors of Breusch and Pagan, implemented in @mvreg@, and the Doornik- Hansen omnibus test for multivariate normality, implemented in @omninorm@.
These tests make use of Stata's matrix language; it may be necessary to use ^set matsize^ to increase the default matrix size before reading in the dat > a.
^dfk^ specifies the use of an alternate divisor in computing the covariance matrix for the equation errors. As an asymptotically justified estimator, ^vecar6^ by default uses the number of sample observations (T) as a divisor. When the dfk option is set, a small-sample adjustment is made and the divisor is taken to be sqrt(T - k).
^noheader^ suppresses display of the table reporting F statistics, R-squared, and root mean square error above the coefficient table.
^table^ displays the full coefficient table.
^level(^#^)^ specifies the confidence level, in percent, for confidence interva > ls; see help @level@.
^saving(^name^)^ specifies that the log determinant of the residual covariance matrix associated with this model is to be saved as ^name^.
^using(^name^)^ specifies the name of the model against which this model is to > be tested. The saved model should have a greater lag length, so that the likelihood ratio test compares the more general saved model with the restricted model currently estimated.
^uncorr^ specifies that the likelihood ratio tests for lag length implemented b > y ^saving^ and ^using^, as well as the test against the zero-order model implemented by ^cov^, are to be conducted without the adjustment for degree > s of freedom advocated by Sims (1980). Without this option, the difference between log determinants of the respective covariance matrices is scaled by (T-c), where T is the number of observations and c is the number of regressors in each of the unrestricted model's equations. With the ^uncorr^ option, the multiplier is merely T.
Options for @predict@ -------------------
^equation(^eqno^)^ specifies to which equation you are referring.
^equation()^ is filled in with one ^eqno^ for options ^xb^, ^stdp^, ^residu > als^. ^equation(#1)^ would mean the calculation is to be made for the first equation, ^equation(#2)^ would mean the second, and so on. Alternatively, you could refer to the equations by their names. ^equation(income)^ would refer to the equation named income and ^equation(hours)^ to the equation named hours.
If you do not specify ^equation()^, results are as if you specified ^equation(#1)^.
^stddp^ and ^difference^ refer to between-equation concepts. To use these options, you must specify ^equation(#1,#2)^ or ^equation(income,hours)^. Wh > en two equations must be specified, ^equation()^ is not optional.
^xb^ the default, calculates the linear prediction from the estimated model.
^stdp^ calculates the standard error of the linear prediction.
^residuals^ calculates the residuals.
^difference^ calculates the difference between the linear predictions of two equations in the system.
^stddp^ calculates the standard error of the difference in linear predictions between two equations.
Examples --------
. ^use http://fmwww.bc.edu/ec-p/data/macro/wgmacro6.dta,clear^
. ^vecar6 dlinv dlinc dlcnsump, maxlag(2)^ . ^vecar6 dlinv dlinc dlcnsump, maxlag(2) table exog(qtr) cov^ . ^predict ihat, eq(dlinv)^ . ^predict ieps, resid eq(dlinv)^ . ^mat list e(Sigma)^ . ^dis "Log-likelihood with `e(maxlag)' lags: `e(ll)'"^ . ^vecar6 dlinv dlinc dlcnsump if tin(1965q1,), maxlag(3) exog(qtr)^
To reproduce Lutkepohl, 1993, Table 4.4:
. ^vecar6 dlinv dlinc dlcnsump if tin(1961q2,1978q4),^ > ^maxlag(4) saving(4) uncorr^ . ^vecar6 dlinv dlinc dlcnsump if tin(1961q2,1978q4),^ > ^maxlag(3) using(4) saving(3) uncorr^ . ^vecar6 dlinv dlinc dlcnsump if tin(1961q2,1978q4),^ > ^maxlag(2) using(3) saving(2) uncorr^ . ^vecar6 dlinv dlinc dlcnsump if tin(1961q2,1978q4),^ > ^maxlag(1) using(2) uncorr^
References ----------
Lutkepohl, Helmut, 1993. Introduction to Multiple Time Series Analysis, 2d ed. Berlin: Springer-Verlag.
Sims, Christopher, 1980. Macroeconomics and Reality. Econometrica 48, 1-49.
Acknowledgements ----------------
This adaptation of vecar (for Stata 6) has been written by Pat Joly. Thanks to Vince Wiggins for assistance modifying this code to interact properly with predict, and to Richard Sperling for developing the AIC, BIC, HQ criteria code.
Authors -------
Christopher F Baum, Boston College, USA, baum@@bc.edu Patrick Joly, Industry Canada, pat.joly@@utoronto.ca
Also see --------
On-line: help for @est@, @reg3@, @mvreg@, @wntstmvq@ (if installed), @omninorm@ (if installed), @regress@, @predict@