We provide in this paper asymptotic theory for the multivariate GARCH (p,q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau  in conjunction with a result given by Boussama  concerning the existence of a stationary and ergodic solution to the multivariate GARCH (p,q) process. We prove asymptotic normality of the quasi-MLE when the initial state is either stationary or ﬁxed.
Comte, F. and Lieberman, Offer, "Asymptotic Theory for Multivariate GARCH Processes" (2001). Cowles Foundation Discussion Papers. 1613.