A Novel Approach to the Estimation of the Long-Range Dependence Parameter

We present a new method to estimate the Hurst parameter of certain classes of random processes. Our 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. We compare the performance of the new method to that of the widely-used wavelet method, and demonstrate that the former is much faster and produces much smaller confidence intervals of the long-range dependence parameter. We believe that the new method can be used as an on-line estimation tool for H and be incorporated in new TCP algorithms that exploit the known self-similar and long-range dependent nature of network traffic