Hurst Parameter Estimation Using Artificial Neural Networks

Abstract

The Hurst parameter captures the amount of long-range dependence (LRD) in a time series. There are severalmethods to estimate the Hurst parameter, being the most popular: the variance-time plot, the R/S plot, theperiodogram, and Whittle’s estimator. The first three are graphical methods, and the estimation accuracy depends onhow the plot is interpreted and calculated. In contrast, Whittle’s estimator is based on a maximum likelihood techniqueand does not depend on a graph reading; however, it is computationally expensive. A new method to estimate theHurst parameter is proposed. This new method is based on an artificial neural network. Experimental results showthat this method outperforms traditional approaches, and can be used on applications where a fast and accurateestimate of the Hurst parameter is required, i.e., computer network traffic control. Additionally, the Hurst parameterwas computed on series of different length using several methods. The simulation results show that the proposedmethod is at least ten times faster than traditional methods.