A novel approach to the estimation of the long-range dependence parameter

Abstract

A new method to estimate the Hurst parameter of certain classes of random processes is presented. This method applies to Gaussian processes that are either exactly second-order self-similar or fractional ARIMA. The case of the former is of special interest because local area network traffic is well-known to be of this form. Confidence intervals and bias are obtained for the estimates using the new method. The new method is then applied to pseudo-random data and to real traffic data. The performance of the new method is compared to that of the widely-used wavelet method, which demonstrates that the former is much faster and produces much smaller confidence intervals of the long-range dependence parameter