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Consistent non-Gaussian pseudo maximum likelihood estimators

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  • Fiorentini, Gabriele
  • Sentana, Enrique

Abstract

We characterise the mean and variance parameters that distributionally misspecified maximum likelihood estimators can consistently estimate in multivariate conditionally heteroskedastic dynamic regression models. We also provide simple closed-form consistent estimators for the rest. The inclusion of means and the explicit coverage of multivariate models make our procedures useful not only for GARCH models but also in many empirically relevant macro and finance applications involving VARs and multivariate regressions. We study the statistical properties of our proposed consistent estimators, as well as their efficiency relative to Gaussian pseudo maximum likelihood procedures. Finally, we provide finite sample results through Monte Carlo simulations.

Suggested Citation

  • Fiorentini, Gabriele & Sentana, Enrique, 2018. "Consistent non-Gaussian pseudo maximum likelihood estimators," CEPR Discussion Papers 12682, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:12682
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    Cited by:

    1. Gabriele Fiorentini & Enrique Sentana, 2021. "Specification tests for non‐Gaussian maximum likelihood estimators," Quantitative Economics, Econometric Society, vol. 12(3), pages 683-742, July.
    2. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    3. C. Gouriéroux & A. Monfort & J.‐M. Zakoïan, 2019. "Consistent Pseudo‐Maximum Likelihood Estimators and Groups of Transformations," Econometrica, Econometric Society, vol. 87(1), pages 327-345, January.
    4. Fiorentini, Gabriele & Sentana, Enrique, 2020. "Discrete Mixtures of Normals Pseudo Maximum Likelihood Estimators of Structural Vector Autoregressions," CEPR Discussion Papers 15411, C.E.P.R. Discussion Papers.
    5. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2021. "Moment tests of independent components," Working Papers wp2021_2102, CEMFI.

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    More about this item

    Keywords

    consistency; efficiency; Misspecification;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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