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This paper investigates the asymptotic theory of the quasi-maximumexponential likelihood estimators (QMELE) for ARMA--GARCH models. Under only afractional moment condition, the strong consistency and the asymptoticnormality of the global self-weighted QMELE are obtained. Based on thisself-weighted QMELE, the local QMELE is showed to be asymptotically normal forthe ARMA model with GARCH (finite variance) and IGARCH errors. A formalcomparison of two estimators is given for some cases. A simulation study iscarried out to assess the performance of these estimators, and a real exampleon the world crude oil price is given.

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