S. Ledesma–Orozco*¹, J. Ruiz–Pinales², G. García–Hernández³, G. Cerda–Villafaña⁴, D. Hernández–Fusilier⁵

^1,2,3,4,5 Universidad de Guanajuato, Comunidad de Palo Blanco, C.P.36885 Salamanca, Guanajuato, Mexico. *E–mail: selo@ugto.mx

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.

Keywords: Parameter estimation, time series, network traffic analysis, neural network.

El parámetro de Hurst captura la cantidad de dependencia de rango amplio (LRD) en las series de tiempo. Hay varios métodos para estimar el parámetro de Hurst, siendo los más populares: la gráfica de varianza contra tiempo, la gráfica R/S, el periodograma, y el estimador de Whittle. Los tres primeros son métodos gráficos, y la precisión de la estimación depende de cómo se interprete y calcule la gráfica. Por otro lado, el estimador de Whittle se basa en una técnica de máxima probabilidad y no depende de una lectura gráfica; sin embargo, éste requiere una gran demanda computacional para su cálculo. Se propone un nuevo método para estimar el parámetro de Hurst. Este nuevo método está basado en una red neuronal artificial. Los resultados experimentales muestran que este método supera a los métodos tradicionales, y que puede ser usado en aplicaciones que requieran una estimación precisa y rápida del parámetro de Hurst, por ejemplo en control de tráfico en redes de computadoras. Adicionalmente, el parámetro de Hurst se calculó en series de diferentes tamaños utilizando varios métodos. Los resultados de la simulación muestran que el método propuesto es por lo menos diez veces más rápido que los métodos tradicionales.

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