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Fractal market time

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  • McCulloch, James
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    Abstract

    Ané and Geman (2000) observed that market returns appear to follow a conditional Gaussian distribution where the conditioning is a stochastic clock based on cumulative transaction count. The existence of long range dependence in the squared and absolute value of market returns is a ‘stylized fact’ and researchers have interpreted this to imply that the stochastic clock is self-similar, multi-fractal (Mandelbrot, Fisher and Calvet, 1997) or mono-fractal (Heyde, 1999). We model the market stochastic clock as the stochastic integrated intensity of a doubly stochastic Poisson (Cox) point process of the cumulative transaction count of stocks traded on the New York Stock Exchange (NYSE). A comparative empirical analysis of a self-normalized version of the stochastic integrated intensity is consistent with a mono-fractal market clock with a Hurst exponent of 0.75.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Empirical Finance.

    Volume (Year): 19 (2012)
    Issue (Month): 5 ()
    Pages: 686-701

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    Handle: RePEc:eee:empfin:v:19:y:2012:i:5:p:686-701

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    Web page: http://www.elsevier.com/locate/jempfin

    Related research

    Keywords: Market time deformation; Long range dependent; Stochastic clock; Fractal Activity Time; Doubly stochastic binomial point process;

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    References

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    1. O. E. Barndorff-Nielsen & S. Z. Levendorskii, 2001. "Feller processes of normal inverse Gaussian type," Quantitative Finance, Taylor & Francis Journals, vol. 1(3), pages 318-331.
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    Cited by:
    1. Batten, Jonathan A. & Kinateder, Harald & Wagner, Niklas, 2014. "Multifractality and value-at-risk forecasting of exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 71-81.

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