A wavelet-based approach to the estimation of the Hurst parameter for self-similar data

In this paper we analyse a wavelet based method for the estimation of the Hurst parameter of synthetically-generated self-similar traces, widely used in a great variety of applications, ranging from computer graphics to parsimonious traffic modelling in broadband networks. The aim of this work is to point out the efficiency of multiresolution schemes in the analysis of fractal processes, characterized by similar statistical features over different time scales. To this end we generated a huge amount of data using the random midpoint displacement (RMD) algorithm, a well-known fast technique for the generation of fractional Gaussian noise (fGn) traces. We then evaluated the Hurst parameter of such sequences in the wavelet domain and compared the results with those obtained with more traditional methods, based on the estimation of the fractal dimensional (Higuchi method) and the moments of the aggregated series.