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Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models


  • Theodossiou, Panayiotis
  • McDonald, James B.
  • Hansen, Christian B.


This paper provides a survey of three families of flexible parametric probability density functions (the skewed generalized t, the exponential generalized beta of the second kind, and the inverse hyperbolic sine distributions) which can be used in modeling a wide variety of econometric problems. A figure, which can facilitate model selection, summarizing the admissible combinations of skewness and kurtosis spanned by the three distributional families is included. Applications of these families to estimating regression models demonstrate that they may exhibit significant efficiency gains relative to conventional regression procedures, such as ordinary least squares estimation, when modeling non-normal errors with skewness and/or leptokurtosis, without suffering large efficiency losses when errors are normally distributed. A second example illustrates the application of flexible parametric density functions as conditional distributions in a GARCH formulation of the distribution of returns on the S&P500. The skewed generalized t can be an important model for econometric analysis.

Suggested Citation

  • Theodossiou, Panayiotis & McDonald, James B. & Hansen, Christian B., 2007. "Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 1, pages 1-20.
  • Handle: RePEc:zbw:ifweej:5742

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    References listed on IDEAS

    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. McDonald, James B., 1989. "Partially adaptive estimation of ARMA time series models," International Journal of Forecasting, Elsevier, vol. 5(2), pages 217-230.
    3. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
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    Cited by:

    1. BenSaïda, Ahmed & Slim, Skander, 2016. "Highly flexible distributions to fit multiple frequency financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 203-213.
    2. Larsen, Bradley J. & Oswald, Florian & Reich, Gregor & Wunderli, Dan, 2012. "A test of the extreme value type I assumption in the bus engine replacement model," Economics Letters, Elsevier, vol. 116(2), pages 213-216.
    3. Stephen Norman & Kerk Phillips, 2013. "What is the shape of real exchange rate nonlinearity?," Applied Financial Economics, Taylor & Francis Journals, vol. 23(5), pages 363-375, March.
    4. Kerman, Sean C. & McDonald, James B., 2013. "Skewness–kurtosis bounds for the skewed generalized T and related distributions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2129-2134.
    5. Martin Møller Andreasen, 2008. "Ensuring the Validity of the Micro Foundation in DSGE Models," CREATES Research Papers 2008-26, Department of Economics and Business Economics, Aarhus University.
    6. James Hansen & James McDonald & Panayiotis Theodossiou & Brad Larsen, 2010. "Partially Adaptive Econometric Methods For Regression and Classification," Computational Economics, Springer;Society for Computational Economics, vol. 36(2), pages 153-169, August.
    7. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    8. Steven Caudill, 2012. "A partially adaptive estimator for the censored regression model based on a mixture of normal distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(2), pages 121-137, June.
    9. Martin Browning & Lars Gårn Hansen & Sinne Smed, 2013. "Rational inattention or rational overreaction? Consumer reactions to health news," IFRO Working Paper 2013/14, University of Copenhagen, Department of Food and Resource Economics.

    More about this item


    Partially Adaptive Estimation; Econometric Models;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General


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