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April 2004 The efficiency of the estimators of the parameters in GARCH processes
István Berkes, Lajos Horváth
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Ann. Statist. 32(2): 633-655 (April 2004). DOI: 10.1214/009053604000000120


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.


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István Berkes. Lajos Horváth. "The efficiency of the estimators of the parameters in GARCH processes." Ann. Statist. 32 (2) 633 - 655, April 2004.


Published: April 2004
First available in Project Euclid: 28 April 2004

zbMATH: 1048.62082
MathSciNet: MR2060172
Digital Object Identifier: 10.1214/009053604000000120

Primary: 62F12
Secondary: 62M10

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

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 2 • April 2004
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