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Department of Applied Finance and Actuarial Studies

James McCulloch Seminar

Past Seminar from the archive

  • Topic: Fractal Market Time
An'e 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 (Cox) Poisson 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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