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

A new model-testing paradigm is introduced. This paradigm is illustrated through the two long-range dependent models: Second-order self-similar, and fractional ARIMA. We then consider the parameter-estimation problem when the process is known to follow a certain model. We illustrate this new estimation method on the two aforementioned long-range dependent models. The confidence intervals and biasedness are obtained for the estimates using the new method. This 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 estimate. We believe that the new method can be used as an on-line estimation tool for the long-range dependence parameter and thus be incorporated in the new TCP algorithms that exploit the known self-similar and long-range dependent nature of network traffic.