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Fractal Market Time

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  • James McCulloch

Abstract

Ane 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.

Suggested Citation

  • James McCulloch, 2012. "Fractal Market Time," Research Paper Series 311, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:311
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp311.pdf
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    References listed on IDEAS

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    Cited by:

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    2. Cao, Guangxi & Jiang, Min & He, LingYun, 2018. "Comparative analysis of grey detrended fluctuation analysis methods based on empirical research on China’s interest rate market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 156-169.

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