Multivariate Ljung-Box portmanteau (Q) test for white noise -----------------------------------------------------------
^wntstmvq^ varlist [^if^ exp] [^in^ range] [^,^ ^L^ags^(^#^)^ ^V^arlags^(^ > #^)^]
^wntstmvq^ is for use with time-series data. You must ^tsset^ your data before using ^wntstmvq^; see help @tsset@. The sample may not contain gaps.
varlist may contain time-series operators; see help @varlist@.
Description -----------
^wntstmvq^ performs the multivariate Ljung-Box portmanteau (or Q) test for white noise in a set of timeseries. This test is a generalization of the univariate Ljung-Box portmanteau (Q) test implemented in Stata as ^wntestq^. The multivariate form of the test is described in Lutkepohl (1993).
The null hypothesis of the multivariate test is that the autocorrelation functions of all series in ^varlist^ have no significant elements for lags 1-^lags^. The ^lags^ parameter may be specified by the user. If the series in ^varlist^ are residuals from a vector autoregression, the ^varlags^ option should be specified to provide the order of the VAR. Under the null hypothesis, the test statistic is distributed Chi-squared with degrees of freedom equal to p^^2 (^lags^-^varlags^) where p is the number of series in ^varlist^. A rejection indicates that at least one series is not white noise.
Although portmanteau statistics are commonly applied in diagnosing time series models, some caution should be exercised with their use in a cointegration context. Jacobson (1995, p. 179) states "[O]ne should exercise some care when using the portmanteau statistic for evaluating the fit of a cointegration model. This observation is due to the facts that cointegration implies the presence of unit roots and an assumption underlying the properties of the portmanteau statistic is that of a stationary process disqualifying roots on the unit circle. There is to my knowledge no theoretical result justifying the use of portmanteau statistics in connection with potential unit roots. Nevertheless these tests are being used..."
Options -------
^lags(^#^)^ specifies the maximum lag order to be used in the test. If not specified, It takes on a default value of min(N/2-2,40) where N is the number of observations available.
^varlags(^#^)^ specifies the order of the VAR (vector autoregression) used to produce the series in ^varlist^. If provided, ^varlags^ must not exceed ^lags^.
Examples --------
. ^wntstmvq eps1 eps2 eps3 eps4^ . ^wntstmvq eps1 eps2 eps3 eps4, lags(24)^ . ^wntstmvq eps1 eps2 eps3 eps4, lags(24) varlags(4)^
References ----------
Jacobson, T. 1995. On the Determination of Lag Order in Vector Autoregressions of Cointegrated Systems. Computational Statistics, 10:177-92.
Lutkepohl, Helmut. Introduction to Multiple Time Series Analysis. 2d ed. 1993. Berlin: Springer-Verlag.
Authors -------
Richard Sperling, The Ohio State University, USA rsperling@@boo.net
Christopher F Baum, Boston College, USA baum@@bc.edu
Also see --------
Manual: ^[R] wntestq^ On-line: help for @wntestq@, @ac@