TESTING FOR SERIAL CORRELATION OF UNKNOWN FORM IN COINTEGRATED TIME SERIES MODELS

摘要

Portmanteau test statistics are useful for checking the adequacy ofmany time series models. Here we generalize the omnibus procedure proposed byDuchesne and Roy (2004, Journal of Multivariate Analysis, 89, 148-180) for multivariatestationary autoregressive models with exogenous variables (VARX) to thecase of cointegrated (or partially nonstationary) VARX models. We show that forcointegrated VARX time series, the test statistic obtained by comparing the spectraldensity of the errors under the null hypothesis of non-correlation with a kernel-basedspectral density estimator, is asymptotically standard normal. The parameters ofthe model can be estimated by conditional maximum likelihood or by asymptoticallyequivalent estimation procedures. The procedure relies on a truncation point or asmoothing parameter. We state conditions under which the asymptotic distributionof the test statistic is unaffected by a data-dependent method. The finite sampleproperties of the test statistics are studied via a small simulation study.