COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1349

Asymptotic Theory for Multivariate GARCH Processes

F. Comte
University of Paris

O. Lieberman
Technion-Israel Institute of Technology and Yale University

 December 2001

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 [19] in conjunction with a result given by Boussama [9] 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.

Keywords: Asymptotic normality, BEKK, Consistency, GARCH, Martingale CLT

JEL Classification: C10, C13