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Quadratic M-Estimators for ARCH-Type Processes

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  • Nour Meddahi

    ()

  • Éric Renault

    ()

Abstract

This paper addresses the issue on 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 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 usual 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. Cet article s'intéresse à l'estimation des modèles semiparamétriques de séries temporelles définis par leur moyenne et variance conditionnelles. Nous mettons en exergue l'importance de l'utilisation jointe des restrictions sur la moyenne et la variance. Ceci amène à tenir compte de la covariance entre la moyenne et la variance ainsi que de la variance de la variance, autrement dit la skewness et la kurtosis. Nous établissons les liens directs entre les méthodes paramétriques usuelles d'estimation, à savoir l'EPMV (Estimateur du Pseudo Maximum de Vraisemblance), les GMM et les M-estimateurs. L'EPMV usuel est, dans le cas de la non-normalité, moins efficace que l'estimateur GMM optimal. Néanmoins, l'EPMV bivarié basé sur le vecteur composé de la variable dépendante et de son carré est aussi efficace que l'estimateur GMM optimal. Une analyse Monte Carlo confirme la pertinence de notre approche, en particulier l'importance de la skewness.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 98s-29.

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Date of creation: 01 Jan 1998
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Handle: RePEc:cir:cirwor:98s-29

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Keywords: M-estimator; QMLE; GMM; heteroskedasticity; conditional skewness and kurtosis; M-estimateur; EPMV; GMM; hétéroscédasticité; skewness et kurtosis conditionnelles;

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Cited by:
  1. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
  2. Ali Alami & Éric Renault, 2001. "Risque de modèle de volatilité," CIRANO Working Papers 2001s-06, CIRANO.
  3. Todd, Prono, 2010. "Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 20034, University Library of Munich, Germany.
  4. Hao Zhou, 2003. "Itô conditional moment generator and the estimation of short rate processes," Finance and Economics Discussion Series 2003-32, Board of Governors of the Federal Reserve System (U.S.).

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