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Goodness of fit test for the multifractal model of asset returns

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  • Bell, Peter

Abstract

This paper explores extensions to the random walk model for time series in finance. There is some disagreement about the suitability of multifractal probability models, but they have compelling attributes. Research that has found no evidence to support the multifractal model has used testing procedures that do not have known statistical power. Therefore, there is an opportunity for new methodology. This paper presents a testing procedure to determine if data follows a multifractal or monofractal process. Using simulation, the paper derives the power of the test. Although the power is low, the test suggests that some observed prices do follow multifractal behaviour. This is a strong result. Further, this work suggests there will be further disagreement in the literature going forward due to the difficulty of identifying multifractal data.

Suggested Citation

  • Bell, Peter, 2012. "Goodness of fit test for the multifractal model of asset returns," MPRA Paper 38689, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:38689
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    File URL: https://mpra.ub.uni-muenchen.de/38689/1/MPRA_paper_38689.pdf
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    References listed on IDEAS

    as
    1. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    2. Lux, Thomas, 2003. "Detecting multi-fractal properties in asset returns: The failure of the scaling estimator," Economics Working Papers 2003-14, Christian-Albrechts-University of Kiel, Department of Economics.
    3. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractality in stock indexes: Fact or Fiction?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3605-3614.
    4. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Statistical methods; fractal geometry; finance;
    All these keywords.

    JEL classification:

    • G0 - Financial Economics - - General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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