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Modeling Financial Series Distributions: A Versatile Data Fitting Approach

Author

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  • JEN S. SHANG

    (Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260-7502, USA)

  • PANDU R. TADIKAMALLA

    (Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260-7502, USA)

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.

Suggested Citation

  • Jen S. Shang & Pandu R. Tadikamalla, 2004. "Modeling Financial Series Distributions: A Versatile Data Fitting Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 231-251.
    • Handle: RePEc:wsi:ijtafx:v:07:y:2004:i:03:n:s0219024904002475
    DOI: 10.1142/S0219024904002475
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    Cited by:

    1. Jaehyuk Choi & Chenru Liu & Byoung Ki Seo, 2019. "Hyperbolic normal stochastic volatility model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(2), pages 186-204, February.
    2. Simon Lalancette & Jean†Guy Simonato, 2017. "The Role of the Conditional Skewness and Kurtosis in VIX Index Valuation," European Financial Management, European Financial Management Association, vol. 23(2), pages 325-354, March.
    3. Simonato, Jean-Guy, 2012. "GARCH processes with skewed and leptokurtic innovations: Revisiting the Johnson Su case," Finance Research Letters, Elsevier, vol. 9(4), pages 213-219.

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