Fractal Market Time

Abstract:     
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.

Number of Pages in PDF File: 41

Keywords: Time Deformation, Long Range Dependent, Stochastic Clock, Fractal Activity Time, New York Stock Exchange, Doubly Stochastic Binomial Point Process

JEL Classification: G10, C22

working papers series