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Quadratic M-Estimators for ARCH-Type Processes

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  • Nour Meddahi
  • Eric Renault

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.
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Suggested Citation

  • Nour Meddahi & Eric Renault, 1998. "Quadratic M-Estimators for ARCH-Type Processes," CIRANO Working Papers 98s-29, CIRANO.
    • Handle: RePEc:cir:cirwor:98s-29
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    4. Hao Zhou, 2003. "Itô Conditional Moment Generator and the Estimation of Short-Rate Processes," Journal of Financial Econometrics, Oxford University Press, vol. 1(2), pages 250-271.
    5. Todd, Prono, 2010. "Simple GMM Estimation of the Semi-Strong GARCH(1,1) Model," MPRA Paper 20034, University Library of Munich, Germany.

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    More about this item

    Keywords

    M-estimator; QMLE; GMM; heteroskedasticity; conditional skewness and kurtosis; M-estimateur; EPMV; GMM; hétéroscédasticité; skewness et kurtosis conditionnelles;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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