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)
Pages: 42 pages
Date: 2012-08-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published as: McCulloch, J., 2012, "Fractal Market Time", Journal of Empirical Finance, 19(5), 686-701.

Downloads: (external link)
https://www.uts.edu.au/sites/default/files/qfr-archive-03/QFR-rp311.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:uts:rpaper:311

Access Statistics for this paper

More papers in Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Duncan Ford ().