Analysis of self-similar data by artificial neural networks

Long range dependence is closely linked with self-similar stochastic processes and random fractals, which have been considered extensively for signal processing applications and computer network traffic modeling. The Hurst parameter captures the amount of long-range dependence in a time series. Typically, the analysis of self-similar series is performed using: the variance-time plot, the R/S plot, the periodogram, and Whittle´s estimator. The first three are graphical methods, and their accuracy depends strongly on the interpretation of the plot. Whittle´s estimator is based on a maximum likelihood technique and offers excellent results; however it is computationally pricey. A new method to estimate the Hurst parameter using artificial neural networks is proposed. Experimental results show that this method outperforms conventional approaches, and can be used on applications where a quick and precise analysis of self-similar data is required.