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Fourth Order Pseudo Maximum Likelihood Methods

Author

Listed:
  • Alberto HOLLY

    (Institute of Health Economics and Management (IEMS) and University of Lausanne)

  • Alain MONFORT

    (CNAM and CREST)

  • Michael ROCKINGER

    (Swiss Finance Institute, University of Lausanne and CEPR)

Abstract

The objective of this paper is to extend the results on Pseudo Maximum Likelihood (PML) theory derived in Gourieroux, Monfort, and Trognon (GMT) (1984) to a situation where the first four conditional moments are specified. Such an extension is relevant in light of pervasive evidence that conditional distributions are non-Gaussian in many economic situations. The key statistical tool here is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in GMT(1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed which shows, in particular, that the QGPML2 method reaches the semi-parametric bound. The key numerical tool that we use is the Gauss-Freud integration scheme which solves a computational problem that has previously been raised in several econometric fields. Simulation exercises show the feasibility and robustness of the methods.

Suggested Citation

  • Alberto HOLLY & Alain MONFORT & Michael ROCKINGER, 2009. "Fourth Order Pseudo Maximum Likelihood Methods," Swiss Finance Institute Research Paper Series 09-23, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp0923
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    2. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.
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    More about this item

    Keywords

    Quartic Exponential Family; Pseudo Maximum Likelihood; Skewness; Kurtosis.;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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