Asymptotic theory for multivariate GARCH processes

Authors:
F. Comte;O. Lieberman
Affiliations:
Laboratoire MAP5, FRE CNRS 2428, University of Paris 5, France;Faculty of Industrial Engineering and Management, Technion--Israel Institute of Technology, Haifa, Israel
Venue:
Journal of Multivariate Analysis
Year:
2003

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Abstract

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 by Jeantheau (Econometric Theory 14 (1998), 70) in conjunction with a result given by Boussama (Ergodicity, mixing and estimation in GARCH models, Ph.D. Dissertation, University of Paris 7, 1998) 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.