Eur. Phys. J. B (2012) 85: 86
https://doi.org/10.1140/epjb/e2012-20803-2

Regular Article

Introducing fractal dimension algorithms to calculate the Hurst exponent of financial time series

¹ Area of Geometry and Topology, Faculty of Science, Universidad de Almería, 04120 Almería, Spain
² Department of Accounting and Finance, Faculty of Economics and Business, Universidad de Almería, 04120 Almería, Spain

^a e-mail: jetrini@ual.es

Received: 30 September 2011
Received in final form: 24 December 2011
Published online: 5 March 2012

Abstract

In this paper, three new algorithms are introduced in order to explore long memory in financial time series. They are based on a new concept of fractal dimension of a curve. A mathematical support is provided for each algorithm and its accuracy is tested for different length time series by Monte Carlo simulations. In particular, in the case of short length series, the introduced algorithms perform much better than the classical methods. Finally, an empirical application for some stock market indexes as well as some individual stocks is presented.