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August 2011 Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA–GARCH/IGARCH models
Ke Zhu, Shiqing Ling
Ann. Statist. 39(4): 2131-2163 (August 2011). DOI: 10.1214/11-AOS895

Abstract

This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA–GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given for some cases. A simulation study is carried out to assess the performance of these estimators, and a real example on the world crude oil price is given.

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Ke Zhu. Shiqing Ling. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA–GARCH/IGARCH models." Ann. Statist. 39 (4) 2131 - 2163, August 2011. https://doi.org/10.1214/11-AOS895

Information

Published: August 2011
First available in Project Euclid: 26 October 2011

zbMATH: 1227.62076
MathSciNet: MR2893864
Digital Object Identifier: 10.1214/11-AOS895

Subjects:
Primary: 62F12 , 62M10 , 62P20

Keywords: ARMA–GARCH/IGARCH model , asymptotic normality , global self-weighted/local quasi-maximum exponential likelihood estimator , strong consistency

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 4 • August 2011
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