The Annals of Statistics

The efficiency of the estimators of the parameters in GARCH processes

István Berkes and Lajos Horváth

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We propose a class of estimators for the parameters of a GARCH(p,q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the innovations is polynomial, even a quasi-maximum likelihood estimator based on exponential density performs better than the standard normal density-based quasi-likelihood estimator of Lee and Hansen and Lumsdaine.

Article information

Ann. Statist. Volume 32, Number 2 (2004), 633-655.

First available in Project Euclid: 28 April 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F12: Asymptotic properties of estimators
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

GARCH(p, q) sequence quasi-maximum likelihood asymptotic normality asymptotic covariance matrix Fisher information number


Berkes, István; Horváth, Lajos. The efficiency of the estimators of the parameters in GARCH processes. Ann. Statist. 32 (2004), no. 2, 633--655. doi:10.1214/009053604000000120.

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