  A new portmanteau diagnostic test for vector autoregressive moving average
(VARMA) models that is based on the determinant of the standardized
multivariate residual autocorrelations is derived. The new test statistic may
be considered an extension of the univariate portmanteau test statistic
suggested by Pena and Rodriguez (2002, A Powerful Portmanteau Test of Lack of
Test for Time Series, Journal of American Statistical Association) The
asymptotic distribution of the test statistic is derived as well as a
chi-square approximation. However, the Monte-Carlo test is recommended unless
the series is very long. Extensive simulation experiments demonstrate the
usefulness of this test as well as its improved power performance compared to
widely used previous multivariate portmanteau diagnostic check. Two
illustrative applications are given.
