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

TL;DR

This paper develops and analyzes new estimators for ARMA-GARCH models, demonstrating their consistency and normality under weak conditions, with practical validation through simulations and real data application.

Contribution

Introduces global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH models, establishing their asymptotic properties under fractional moments.

Findings

Global self-weighted QMELE is strongly consistent and asymptotically normal.

Local QMELE is asymptotically normal for ARMA-GARCH and IGARCH models.

Simulation and real data analysis validate estimator performance.

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.