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2004•BernoulliOpen access

Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes

Christian Francq, Jean‐Michel Zakoïan

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Abstract

We prove the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of pure generalized autoregressive conditional heteroscedastic (GARCH) processes, and of autoregressive moving-average models with noise sequence driven by a GARCH model. Results are obtained under mild conditions.

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What this paper is about

We prove the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of pure generalized autoregressive conditional heteroscedastic (GARCH) processes, and of autoregressive moving-average models with noise sequence driven by a GARCH model. Results are obtained under mild conditions.

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Available abstract

We prove the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of pure generalized autoregressive conditional heteroscedastic (GARCH) processes, and of autoregressive moving-average models with noise sequence driven by a GARCH model. Results are obtained under mild conditions.

Key concepts: Mathematics, Autoregressive conditional heteroskedasticity, Heteroscedasticity, Autoregressive model, Estimator, Strong consistency, Asymptotic distribution, Consistency (knowledge bases)

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