Itô’s Excursion Theory, the Hurst Coefficient, and Fractional Excursions in Finance

29 Pages Posted: 4 Apr 2012

See all articles by Paitoon Wongsasutthikul

Paitoon Wongsasutthikul

Cornell University - School of Applied Economics and Management

Calum G. Turvey

Cornell University - School of Applied Economics and Management

Date Written: April 4, 2012

Abstract

In this paper, we investigate how Itô’s excursion theory can be usefully applied to economic time series data (Itô 2007). We relate excursion theory to geometric and fractional Brownian motion and the Hurst coefficient. We then calculate the Hurst coefficient for all stocks on the DOW 30, S&P 500 and Russell 2000, showing the distribution of Hurst measures and relating them statistically to excursions. In doing so we provide a nice and intuitive link between Brownian motion and excursions, an application and consequence that we have not seen before.

Keywords: Ito Excursion, Hurst Coefficient, Fractional Brownian Motion, Quantitative Finance

JEL Classification: G10, G12, G14

Suggested Citation

Wongsasutthikul, Paitoon and Turvey, Calum G., Itô’s Excursion Theory, the Hurst Coefficient, and Fractional Excursions in Finance (April 4, 2012). Available at SSRN: https://ssrn.com/abstract=2034472 or http://dx.doi.org/10.2139/ssrn.2034472

Paitoon Wongsasutthikul

Cornell University - School of Applied Economics and Management ( email )

248 Warren Hall
Ithaca, NY 14853
United States

Calum G. Turvey (Contact Author)

Cornell University - School of Applied Economics and Management ( email )

248 Warren Hall
Ithaca, NY 14853
United States

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