Tukey-type Distributions in the context of financial data - Fischer, Matthias; Klein, Ingo; Horn, Armin (Communications in Statistics-Theory and Methods, 2007)
Using the Gaussian distribution as probabilistic model for (leptokurtic) financial data is widespread, 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 the standard normal distribution or, more generally, of a symmetric "parent" distribution Z and allow for leptokurtosis represented by the (elongation) parameter H > 0. Alternatively, the J-distributions of Fischer and Klein (2004) or the K-distributions of Haynes et al. (1997) may be applied. In order to additionally introduce skewness, some have these distribution families have been generalized subsequently. Within this work we "complete" the class of so-called Tukey-type distributions by introducing KQ- and JQ-distributions, on the one side, and KK-, JJ-, and [image omitted]-distributions, on the other side. Moreover, we investigate the goodness-of-fit of such Tukey-type distributions for different parent distributions Z in the context of financial return data. In particular, the interplay between Z and different transformations is focussed. Finally, our results are compared to those of popular multi-parametric distribution model
WiSo-Import:2015-03-26:993
Keywords: Financial return data; Kurtosis; Normal transformation; Skewness; Variable transformation