Quadratic M-Estimators for ARCH-Type Processes

Nour MEDDAHI and Éric RENAULT

Cahiers de recherche from Universite de Montreal, Departement de sciences economiques

Abstract: This paper addresses the issue of estimating semiparametric time series models specified by their conditional mean and conditional variance. We stress the importance of using joint restrictions on the mean and variance. This leads us to take into account the covariance between the mean and the variance and the variance of the variance, that is, the skewness and kurtosis. We establish the direct links between the usual parametric estimation methods, namely, the QMLE, the GMM and the M-estimation. The ususal univariate QMLE is, under non-normality, less efficient than the optimal GMM estimator. However, the bivariate QMLE based on the dependent variable and its square is as efficient as the optimal GMM one. A Monte Carlo analysis confirms the relevance of our approach, in particular, the importance of skewness.

Keywords: M-estimator; QMLE; GMM; heteroskedasticity; conditional skewness and kurtosis (search for similar items in EconPapers)
JEL-codes: C30 C32 C13 (search for similar items in EconPapers)
Date: Written 1998
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Persistent link: http://EconPapers.repec.org/RePEc:mtl:montde:9814

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