MODELING FINANCIAL SERIES DISTRIBUTIONS: A VERSATILE DATA FITTING APPROACH

Abstract

The empirical distribution of common stock returns is a subject of interest to many researchers, as it often determines the validity of theoretical models proposed in the economics and finance studies. This paper brings to the attention the availability of two flexible systems of distributions for fitting data: the Johnson system of distributions and the Tadikamalla–Johnson system of distributions. We explore the feasibility of fitting the empirical distributions of several financial series to these two systems of distributions. Both systems of distributions are highly flexible and capable of accommodating all possible skewness and kurtosis values. The probability density function and the cumulative distribution function take on simple closed forms and appropriate transformations of the data lead to normal/logistic distributions. In addition, the parameter estimation procedures are easy to implement. When the results are compared with those of other data fitting models, in all cases tested, the proposed distributions provide a good fit to the empirical distribution of data.