Itô’s Excursion Theory, the Hurst Coefficient, and Fractional Excursions in Finance
29 Pages Posted: 4 Apr 2012
Date Written: April 4, 2012
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: Suggested Citation