Regular variation and related results for the multivariate GARCH(p,q)(p,q) model with constant conditional correlations

We establish the regular variation of the finite dimensional distributions of the multivariate GARCH(p,q)(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.