Improved multivariate portmanteau test

TL;DR

This paper introduces an improved multivariate portmanteau test for VARMA models based on the determinant of standardized residual autocorrelations, showing enhanced power over existing methods through simulations and applications.

Contribution

It develops a new portmanteau test extending univariate methods to multivariate models, with derived asymptotic distribution and practical Monte-Carlo implementation.

Findings

The new test has superior power compared to existing diagnostics.

Monte-Carlo test is recommended for practical use.

The test performs well in simulation and real data applications.

Abstract

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.