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Tukey-type distributions in the context of financial data

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  • Fischer, Matthias J.
  • Horn, Armin
  • Klein, Ingo

Abstract

Using the Gaussian distribution as statistical model for data sets is widely spread, especially in practice. However, departure from normality seems to be more the rule than the exception. The H-distributions, introduced by Tukey (1960, 1977), are generated by a single transformation (H-transformation) of a standard normal distribution (or, more general, of a symmetric distribution) Z and allow for leptokurtosis represented by the (elongation) parameter h > 0. In order to additionally take skewness into account by means of certain transformations, several generalizations and extensions (HQ,HH,GH,GK;...) have been proposed in the literature. Within this work we 'complete' this class of Tukey-type distributions by introducing KQ- and JQ-distributions on the one side and KK-, JJ- and e GJ-distributions on the other side. Moreover, we empirically compare the goodness-of-fit of such Tukey-type distributions for different symmetrical distributions Z (here: Gaussian, logistic and hyperbolic secant distribution) in the context of financial return data. In particular, the interplay between Z and the Tukey-type transformations is investigated. Finally, results are compared to those of popular multi-parametric distribution models with closedform densities.

Suggested Citation

  • Fischer, Matthias J. & Horn, Armin & Klein, Ingo, 2003. "Tukey-type distributions in the context of financial data," Discussion Papers 52/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    • Handle: RePEc:zbw:faucse:522003
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    References listed on IDEAS

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    1. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    2. McDonald, James B., 1991. "Parametric models for partially adaptive estimation with skewed and leptokurtic residuals," Economics Letters, Elsevier, vol. 37(3), pages 273-278, November.
    3. Badrinath, S G & Chatterjee, Sangit, 1991. "A Data-Analytic Look at Skewness and Elongation in Common-Stock-Return Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 223-233, April.
    4. Fischer, Matthias J. & Klein, Ingo, 2003. "Kurtosis modelling by means of the J-transformation," Discussion Papers 51/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    5. Badrinath, S G & Chatterjee, Sangit, 1988. "On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index," The Journal of Business, University of Chicago Press, vol. 61(4), pages 451-472, October.
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    1. Klein, Ingo & Fischer, Matthias J., 2003. "Kurtosis transformation and kurtosis ordering," Discussion Papers 53/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    2. Fischer, Matthias J. & Klein, Ingo, 2003. "Kurtosis modelling by means of the J-transformation," Discussion Papers 51/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.

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