Asymptotic theory for multivariate GARCH processes

F. Comte, O. Lieberman

Research output: Contribution to journalReview articlepeer-review

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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.

Original languageEnglish
Pages (from-to)61-84
Number of pages24
JournalJournal of Multivariate Analysis
Issue number1
StatePublished - Jan 2003
Externally publishedYes


  • Asymptotic normality
  • BEKK
  • Consistency
  • Martingale CLT


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