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Fractal market time

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  • McCulloch, James

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.

Suggested Citation

  • McCulloch, James, 2012. "Fractal market time," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 686-701.
    • Handle: RePEc:eee:empfin:v:19:y:2012:i:5:p:686-701
    DOI: 10.1016/j.jempfin.2012.08.001
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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.
    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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    More about this item

    Keywords

    Market time deformation; Long range dependent; Stochastic clock; Fractal Activity Time; Doubly stochastic binomial point process;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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