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2003•BernoulliOpen access

GARCH processes: structure and estimation

I. Berkés, Lajos H. Horvath, Piotr S. Kokoszka

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Abstract

We study the structure of a GARCH$(p,q)$ sequence. We show that the conditional variance can be written as an infinite sum of the squares of the previous observations and that the representation is unique. We prove the consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of the GARCH$(p,q)$ sequence under mild conditions.

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What this paper is about

We study the structure of a GARCH$(p,q)$ sequence. We show that the conditional variance can be written as an infinite sum of the squares of the previous observations and that the representation is unique. We prove the consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of the GARCH$(p,q)$ sequence under mild conditions.

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Available abstract

We study the structure of a GARCH$(p,q)$ sequence. We show that the conditional variance can be written as an infinite sum of the squares of the previous observations and that the representation is unique. We prove the consistency and asymptotic normality of the quasi-maximum likelihood estimator of the parameters of the GARCH$(p,q)$ sequence under mild conditions.

Key concepts: Mathematics, Autoregressive conditional heteroskedasticity, Estimator, Asymptotic distribution, Consistency (knowledge bases), Strong consistency, Sequence (biology), Conditional variance

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