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

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

2012-01-30

arxiv.org/abs/1201.6216v1

Annals of Statistics 2011, Vol. 39, No. 4, 2131-2163

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS895 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/11-AOS895

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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