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Fractal Market Time

James McCulloch

No 311, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: market time deformation; long range dependent; stochastic clock; fractal activity time; doubly stochastic binomial point process (search for similar items in EconPapers)
Date: 2012-08-01
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Published as: McCulloch, J., 2012, "Fractal Market Time", Journal of Empirical Finance, 19(5), 686-701.

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