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2003•RePEc: Research Papers in EconomicsRequires access

Asymptotic Theory for Multivariate GARCH Processes

Fabienne Comte, Offer Lieberman

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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 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.

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What this paper is about

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.

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Available 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 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.

Key concepts: Mathematics, Asymptotic distribution, Multivariate statistics, Estimator, Ergodic theory, Autoregressive conditional heteroskedasticity, Consistency (knowledge bases), Strong consistency

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