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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 location-scale models, and provide simple closed-form consistent estimators for the rest. Including means and a multivariate coverage make our procedures useful for Garch-M models and 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 and semiparametric procedures. We provide finite sample results through Monte Carlo simulations. Finally, we discuss two practical applications to individual stock returns and mean–variance efficiency/spanning tests.

Suggested Citation

  • Fiorentini, Gabriele & Sentana, Enrique, 2019. "Consistent non-Gaussian pseudo maximum likelihood estimators," Journal of Econometrics, Elsevier, vol. 213(2), pages 321-358.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:2:p:321-358
    DOI: 10.1016/j.jeconom.2019.05.017
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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. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "Moment tests of independent components," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(1), pages 429-474, May.
    5. Fiorentini, Gabriele & Sentana, Enrique, 2023. "Discrete mixtures of normals pseudo maximum likelihood estimators of structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 235(2), pages 643-665.
    6. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "PML vs minimum χ 2 : the comeback," Working Papers wp2022_2210, 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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