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Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models

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

Abstract

This paper discusses three families of flexible parametric probability density functions: the skewed generalized t, the exponential generalized beta of the second kind, and the inverse hyperbolic sin distributions. These families allow quite flexible modeling the first four moments of a distribution and could be considered in modeling a wide variety of economic problems. We illustrate their use in a simple regression model with a simulation study that demonstrates that the use of the flexible distributions may result in significant efficiency gains relative to more conventional regression procedures, such as ordinary least squares or least absolute deviations regression, without a suffering from a large efficiency loss when errors are Gaussian.

Suggested Citation

  • Theodossiou, Panayiotis & McDonald, James B. & Hansen, Christian B., 2007. "Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models," Economics Discussion Papers 2007-13, Kiel Institute for the World Economy.
    • Handle: RePEc:zbw:ifwedp:5527
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    Cited by:

    1. Joe Hirschberg & Jenny Lye, 2021. "Estimating risk premiums for regulated firms when accounting for reference-day variation and high-order moments of return volatility," Environment Systems and Decisions, Springer, vol. 41(3), pages 455-467, September.
    2. Randall A. Lewis & James B. McDonald, 2014. "Partially Adaptive Estimation of the Censored Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 732-750, October.
    3. 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.
    4. 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.
    5. Yeliz Mert Kantar & Ilhan Usta & Şükrü Acıtaş, 2011. "A Monte Carlo simulation study on partially adaptive estimators of linear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1681-1699, August.
    6. 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.
    7. 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.
    8. Sikora, Grzegorz & Michalak, Anna & Bielak, Łukasz & Miśta, Paweł & Wyłomańska, Agnieszka, 2019. "Stochastic modeling of currency exchange rates with novel validation techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1202-1215.
    9. Monique Graf & J. Miguel Marín & Isabel Molina, 2019. "A generalized mixed model for skewed distributions applied to small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 565-597, June.
    10. 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.
    11. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    12. Szarek, Dawid & Bielak, Łukasz & Wyłomańska, Agnieszka, 2020. "Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    13. Higbee, Joshua D. & McDonald, James B., 2024. "A comparison of the GB2 and skewed generalized log-t distributions with an application in finance," Journal of Econometrics, Elsevier, vol. 240(2).
    14. 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.
    15. Martin Browning & Lars Gårn Hansen & Sinne Smed, 2019. "Heterogeneous Consumer Reactions to Health News," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 101(2), pages 579-599.
    16. 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.
    17. Herrmann Klaus & Fischer Matthias, 2010. "An Alternative Maximum Entropy Model for Time-Varying Moments with Application to Financial Returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(3), pages 1-23, May.
    18. 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.

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    Keywords

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    JEL classification:

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

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