Abstract
Abstract In this paper we derive a semiparametric efficient adaptive estimator for the GJR-GARCH ( 1 , 1 ) {(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 ) {(1,1)} model with respect to the unknown distribution of the innovation.
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