Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA–GARCH/IGARCH models
The Annals of Statistics · 2011 · Volume 39 · Issue 4
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.
Keywords
62F12, 62M10, 62P20, ARMA–GARCH/IGARCH model, asymptotic normality, global self-weighted/local quasi-maximum exponential likelihood estimator, strong consistency
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