Diagnostic checking of nonlinear multivariate time series with multivariate arch errors

Multivariate time series with multivariate ARCH errors have been found useful in many applications. In order to check the adequacy of these models, we define the sum of squared (standardized) residual autocorrelations and derive their asymptotic distribution. The results are used to derive several new multivariate portmanteau tests. Simulation results show that the asymptotic standard errors are quite satisfactory compared with empirical standard errors and that the tests have reasonable empirical size and power. The distribution of the standardized residual autocorrelations is also derived.