Asymptotic theory for multivariate GARCH processes

F. Comte and O. Lieberman

Journal of Multivariate Analysis, 2003, vol. 84, issue 1, 61-84

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.

Keywords: Asymptotic; normality; BEKK; Consistency; GARCH; Martingale; CLT (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (208)

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