Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Asymptotic theory for multivariate GARCH processes


Code(s) de Classification MSC:

Résumé: 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 [12] in conjunction with a result given by Boussama [7] 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. The proofs employ much weaker conditions than those imposed by Lumsdaine [15], who was restricted to the univariate GARCH(1,1) and IGARCH(1,1) cases.

Mots Clés: Asymptotic normality ; BEKK ; Consistency ; GARCH ; Martingale CLT

Date: 2000-05-03

Prépublication numéro: PMA-593