Distribution of the Residual Autocorrelations in Multivariate Arma Time Series Models

SUMMARY The large-sample distribution of the multivariate residual autocorrelations in the vector arma model is derived. This result is somewhat less complicated for the vector autoregressive model. A new multivariate portmanteau test for checking the adequacy of fitted vector arma models is developed. A simulation study shows that a simple modification of the portmanteau test improves its accuracy in small samples.