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Consistent non-Gaussian pseudo maximum likelihood estimators

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  • Sentana, Enrique
  • Fiorentini, Gabriele

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

  • Sentana, Enrique & Fiorentini, Gabriele, 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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    1. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    2. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
    3. Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November.
    4. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-546, October.
    5. Gabriele Fiorentini & Enrique Sentana, 2021. "Specification tests for non‐Gaussian maximum likelihood estimators," Quantitative Economics, Econometric Society, vol. 12(3), pages 683-742, July.
    6. Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, vol. 23(2), pages 251-280, April.
    7. Huberman, Gur & Kandel, Shmuel, 1987. "Mean-Variance Spanning," Journal of Finance, American Finance Association, vol. 42(4), pages 873-888, September.
    8. Keith Vorkink & Douglas J. Hodgson & Oliver Linton, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639.
    9. Amengual, Dante & Fiorentini, Gabriele & Sentana, Enrique, 2013. "Sequential estimation of shape parameters in multivariate dynamic models," Journal of Econometrics, Elsevier, vol. 177(2), pages 233-249.
    10. Jobson, J. D. & Korkie, Bob, 1982. "Potential performance and tests of portfolio efficiency," Journal of Financial Economics, Elsevier, vol. 10(4), pages 433-466, December.
    11. Francq, Christian & Lepage, Guillaume & Zakoïan, Jean-Michel, 2011. "Two-stage non Gaussian QML estimation of GARCH models and testing the efficiency of the Gaussian QMLE," Journal of Econometrics, Elsevier, vol. 165(2), pages 246-257.
    12. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    13. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    14. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2017. "Identification and estimation of non-Gaussian structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 196(2), pages 288-304.
    15. Gibbons, Michael R & Ross, Stephen A & Shanken, Jay, 1989. "A Test of the Efficiency of a Given Portfolio," Econometrica, Econometric Society, vol. 57(5), pages 1121-1152, September.
    16. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    17. MEDDAHI, Nour & RENAULT, Éric, 1998. "Quadratic M-Estimators for ARCH-Type Processes," Cahiers de recherche 9814, Universite de Montreal, Departement de sciences economiques.
    18. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    19. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    20. Javier Mencía & Enrique Sentana, 2012. "Distributional Tests in Multivariate Dynamic Models with Normal and Student-t Innovations," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 133-152, February.
    21. Gabriele Fiorentini & Enrique Sentana, 2007. "On the efficiency and consistency of likelihood estimation in multivariate conditionally heteroskedastic dynamic regression models," Working Paper series 38_07, Rimini Centre for Economic Analysis.
    22. Amengual, Dante & Sentana, Enrique, 2010. "A comparison of mean-variance efficiency tests," Journal of Econometrics, Elsevier, vol. 154(1), pages 16-34, January.
    23. Jianqing Fan & Lei Qi & Dacheng Xiu, 2014. "Quasi-Maximum Likelihood Estimation of GARCH Models With Heavy-Tailed Likelihoods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 178-191, April.
    24. Pietro BALESTRA & Alberto HOLLY, 1990. "A General Kronecker Formula for the Moments of the Multivariate Normal Distribution," Cahiers de Recherches Economiques du Département d'économie 9002, Université de Lausanne, Faculté des HEC, Département d’économie.
    25. Sun, Yiguo & Stengos, Thanasis, 2006. "Semiparametric efficient adaptive estimation of asymmetric GARCH models," Journal of Econometrics, Elsevier, vol. 133(1), pages 373-386, July.
    26. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 945-973.
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    Cited by:

    1. 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.
    2. Gabriele Fiorentini & Enrique Sentana, 2021. "Specification tests for non‐Gaussian maximum likelihood estimators," Quantitative Economics, Econometric Society, vol. 12(3), pages 683-742, July.
    3. 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.
    4. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    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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