{smcl}
{* 24may2002}{...}
{hline}
help for {hi:varlag}{right:[P.Joly]}
{hline}

{title:Statistics to determine the appropriate lag length in VARs, ECMs}

{p 8 26}
{cmd:varlag}
[{it:varlist}]
[{cmd:if} {it:exp}]
[{cmd:in} {it:range}]
{cmd:,}
    {cmdab:l:ags(}{it:#}{cmd:)}
[
    {cmdab:testl:ag(}{it:#}{cmd:)}
    {cmdab:nom:ulti}
    {cmdab:ex:og}({it:varlist})
    {cmdab:t:rend}
    {cmdab:noc:onstant}
    {cmdab:s:ingle}
    {cmdab:nod:etail}
    {cmd:cov}
    {cmdab:cor:r}
    {cmd:large}
    {cmdab:l:evel(}{it:#}{cmd:)}
    {it:vececm_options}
]


{p}
{cmd:varlag} is for use with time-series data.  You must {cmd:tsset}
your data before using these commands; see help {help tsset}.

{p}
{it:varlist} may contain time-series operators; see help
{help varlist}.


{title:Description}

{p}
{cmd:varlag} reports various statistics that are meant to help select
the proper lag structure to use in the estimation of Vector
autoregressions (VARs) and Error Correction Models (ECMs).
For each lag length up to {cmd:lags(}{it:#}{cmd:)}, {cmd:varlag}
reports the Multivariate portmanteau (Ljung-Box) statistic for white
noise residuals, p-values from Omnibus tests of multivariate normality
of the residuals, as well as the Breusch-Pagan statistic for the
independence of residuals between equations.
{cmd:varlag} also performs likelihood ratio tests to test successive
null hypotheses of smaller lag length.

{p}
Whether a varlist is specified determines if the tests should be
computed for a VAR or an ECM.
If varlist is omitted, {cmd:varlag} assumes the tests are for an ECM
and options normally required by {cmd:vececm} must be specified; see
help {help vececm}.
This means that Johansen's ML cointegration rank test must have been
performed prior to running {cmd:varlag}; see help {help johans}.
Otherwise, if varlist is specified, {cmd:varlag} is implemented in the
context of a VAR.

{p}
In the context of a VAR, {cmd:varlag} can report various other
statistics for each individual equation in the system and each lag
length if option {cmd:single} is declared.
It computes the RMSE, FPE, and Schwartz criterion, as well as p-values
of Breusch-Godfrey LM tests for autocorrelated disturbances of order
1, 4, and larger (up to {it:min}[.25*N,{cmd:testlag(}{it:#}{cmd:)}]).
The p-value of the Breusch-Pagan LM statistic for heteroskedasticity
is also reported as an indicator of potential mispecification.
However, the univariate Ljung-Box portmanteau statistic is not
reported as these tests are not appropriate when stochastic regressors
other than lagged values of the dependent variable are included in
individuals regressions.

{p}
For each statistic, the apparent optimal number of lags is reported.


{title:Options}

{p 0 4}
{cmd:lags(}{it:#}{cmd:)} specifies the largest lag length to be
considered.

{p 0 4}
{cmd:testlag(}{it:#}{cmd:)} specifies the largest lag length to use in
LM tests of serial correlation as well as for Multivariate portmanteau
statistics.
The default is for the portmanteau to use {it:min}([N/2]-2,40) and the
LM to use {it:min}(.25*N,40).

{p 0 4}
{cmd:nomulti} suppresses the calculation multivariate statistics for
the system such as Multivariate portmanteau statistics, Omnibus tests
for multivariate normality or residuals (Doornik & Hansen (1994)),
and Breusch-Pagan tests for the independence of the residuals between
equations, i.e., that the disturbance covariance matrix is diagonal.

{p 0 4}
{it:vececm_options} are options used with {cmd:vececm}; see help
{help vececm}.
Options such as {cmd:cir(}{it:#}{cmd:)} and {cmd:sm(}{it:case}{cmd:)}
are required.

{p 0 4}
{cmd:exog(}{it:varlist}{cmd:)} is only allowed in the context of VARs
(i.e. if a varlist is specified) and specifies the exogenous variables
that enter the VAR. {cmd:vececm} takes its exogenous variables from
those specified at {help johans}.

{p 0 4}
{cmd:trend} is only allowed in the context of VARs and specifies that
a linear trend be included in each equation.

{p 0 4}
{cmd:noconstant} is only allowed in the context of VARs and suppresses
the inclusion of an intercept in each equation of the VAR.

{p 0 4}
{cmd:single} is only allowed in the context of VARs and displays
diagnostic statistics for each individual equation in the system, for
each lag length up to {cmd:lags(}{it:#}{cmd:)}.

{p 0 4}
{cmd:nodetail} is relevant only with {cmd:single} and suppresses the
display of individual statistics for every lag length.
Instead, the optimal lag with respect to each statistic is reported.

{p 0 4}
{cmd:cov} requests the display of the variance-covariance matrix of
residuals between equations.

{p 0 4}
{cmd:corr} requests the display of the correlation matrix of residuals
between equations.

{p 0 4}
{cmd:large} specifies that large sample statistics are to be used,
specifically, that the number of sample observations, {it:T}, be used
as a divisor in computing the covariance matrix for the equation
errors rather than alternate divisor, {it:T-K}.
The covariance matrix of equation errors is used in the sequence of
likelihood ratio tests for smaller lag length.
As asymptotically justified estimators, vector autoregressions and
error correction models may use large sample statistics.

{p 0 4}
{cmd:level(}{it:#}{cmd:)} specifies the confidence level, in percent,
for confidence intervals of the coefficients; see help {help level}.


{title:Examples}

{p 8 12}{inp:.} {stata "use http://fmwww.bc.edu/ec-p/data/macro/wgmacro.dta, clear":use http://fmwww.bc.edu/ec-p/data/macro/wgmacro.dta, clear}

{p 8 12}{inp:. varlag investment income consumption, l(8)}

{p 8 12}{inp:. varlag investment income consumption, l(8) single corr}

In Error correction models:

{p 8 12}{inp:. johans investment income consumption, lags(6)}{p_end}
{p 8 12}{inp:. varlag, lags(10) c(1) sm(1)}{p_end}


{title:Author}

Patrick Joly, Industry Canada
pat.joly@utoronto.ca


{title:Also see}

{p 0 19}
On-line:  help for
	{help vecar} (if installed),
	{help vececm} (if installed),
	{help johans} (if installed),
	{help reg3},
	{help wntstmvq},
	{help omninorm}
{p_end}

