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Maximum likelihood estimator for the uneven power distribution: application to DJI returns

Author

Listed:
  • Krzysztof Kontek

    () (Artal Investments, Warsaw)

Abstract

This paper deals with estimating peaked densities over the interval [0,1] using the Un-even Two-Sided Power Distribution (UTP). This distribution is the most complex of all the bounded power distributions introduced by Kotz and van Dorp (2004). The UTP maximum likelihood estimator, a result not derived by Kotz and van Dorp, is presented. The UTP is used to estimate the daily return densities of the DJI and stocks comprising this index. As the returns are found to have high kurtosis values, the UTP provides much more accurate estima-tions than a smooth distribution. The paper presents the program written in Mathematica which calculates maximum likelihood estimators for all members of the bounded power dis-tribution family. The paper demonstrates that the UTP distribution may be extremely useful in estimating peaked densities over the interval [0,1] and in studying financial data.

Suggested Citation

  • Krzysztof Kontek, 2010. "Maximum likelihood estimator for the uneven power distribution: application to DJI returns," Working Papers 43, Department of Applied Econometrics, Warsaw School of Economics.
  • Handle: RePEc:wse:wpaper:43
    as

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    File URL: http://kolegia.sgh.waw.pl/pl/KAE/struktura/IE/struktura/ZES/Documents/Working_Papers/aewp01-10.pdf
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    References listed on IDEAS

    as
    1. Kontek, Krzysztof, 2010. "Estimation of Peaked Densities Over the Interval [0,1] Using Two-Sided Power Distribution: Application to Lottery Experiments," MPRA Paper 22378, University Library of Munich, Germany.
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    More about this item

    Keywords

    Density Distribution; Maximum Likelihood Estimation; Stock Returns;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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