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Fourth order pseudo maximum likelihood methods

Author

Listed:
  • Alberto Holly

    (Faculty of Business and Economics - UNIL - Université de Lausanne = University of Lausanne)

  • Alain Monfort
  • Michael Rockinger

    (UNIL - Université de Lausanne = University of Lausanne)

Abstract

We extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in Gourieroux, Monfort, and Trognon (1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed. The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields. Simulation exercises demonstrate the feasibility and robustness of the methods.

Suggested Citation

  • Alberto Holly & Alain Monfort & Michael Rockinger, 2011. "Fourth order pseudo maximum likelihood methods," Post-Print hal-00815562, HAL.
  • Handle: RePEc:hal:journl:hal-00815562
    DOI: 10.1016/j.jeconom.2011.01.004
    Note: View the original document on HAL open archive server: https://hal.science/hal-00815562
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    6. Giuseppe arbia, 2014. "Least quartic Regression Criterion with Application to Finance," Papers 1403.4171, arXiv.org.
    7. Mauro Bernardi & Leopoldo Catania, 2016. "Portfolio Optimisation Under Flexible Dynamic Dependence Modelling," Papers 1601.05199, arXiv.org.

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    More about this item

    Keywords

    C01; C13; C16; C22; 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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