Semiparametric efficient adaptive estimation of the GJR-GARCH model

Abstract

In this paper we derive a semiparametric efficient adaptive estimator for the GJR-GARCH {(1,1)} model. We first show that the quasi-maximum likelihood estimator is consistent and asymptotically normal for the model used in analysis, and we secondly derive a semiparametric estimator that is more efficient than the quasi-maximum likelihood estimator. Through Monte Carlo simulations, we show that the semiparametric estimator is adaptive for the parameters included in the conditional variance of the GJR-GARCH {(1,1)} model with respect to the unknown distribution of the innovation.