Regular variation and related results for the multivariate GARCH model with constant conditional correlations

We establish the regular variation of the finite dimensional distributions of the multivariate GARCH ( p , q ) process with constant conditional correlations under mild assumptions on the noise distribution. We use this property for two main purposes: First, to describe the componentwise-maximum domain of attraction in which the process lies; and second, to relate the asymptotic behavior of the sample autocovariance function of the process to its regular variation index.