Fractal market time

James McCulloch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)686-701
Number of pages16
JournalJournal of Empirical Finance
Issue number5
Publication statusPublished - 2012


  • Doubly stochastic binomial point process
  • Fractal Activity Time
  • Long range dependent
  • Market time deformation
  • Stochastic clock


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