A Note on Diagnosing Multivariate Conditional Heteroscedasticity Models

In this paper we consider several tests for model misspecification after a multivariate conditional heteroscedasticity model has been fitted. We examine the performance of the recent test due to Ling and Li ( J. Time Ser. Anal. 18 (1997), 447–64), the Box–Pierce test and the residual‐based F test using Monte Carlo methods. We find that there are situations in which the Ling–Li test has very weak power. The residual‐based diagnostics demonstrate significant under‐rejection under the null. In contrast, the Box–Pierce test based on the cross‐products of the standardized residuals often provides a useful diagnostic that has reliable empirical size as well as good power against the alternatives considered.