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.