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 several

methods to estimate the Hurst parameter, being the most popular: the variance-time plot, the R/S plot, the

periodogram, and Whittle’s estimator. The first three are graphical methods, and the estimation accuracy depends on

how the plot is interpreted and calculated. In contrast, Whittle’s estimator is based on a maximum likelihood technique

and does not depend on a graph reading; however, it is computationally expensive. A new method to estimate the

Hurst parameter is proposed. This new method is based on an artificial neural network. Experimental results show

that this method outperforms traditional approaches, and can be used on applications where a fast and accurate

estimate of the Hurst parameter is required, i.e., computer network traffic control. Additionally, the Hurst parameter

was computed on series of different length using several methods. The simulation results show that the proposed

method is at least ten times faster than traditional methods.