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Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models

Zhu, Ke and Ling, Shiqing (2013): Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models. Published in: Annals of Statistics , Vol. 39, No. 4 (2011): pp. 2131-2163.

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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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