Tukey-type distributions in the context of financial data

Matthias J. Fischer, Armin Horn and Ingo Klein

No 52/2003, Discussion Papers from Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics

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.

Keywords: kurtosis; skewness; variable transformation; transformed Gaussian; return data. (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (2)

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