On the wavelet spectrum diagnostic for Hurst parameter estimation in the analysis of Internet traffic

The fluctuations of Internet traffic possess an intricate structure which cannot be simply explained by long–range dependence and self–similarity. In this work, we explore the use of the wavelet spectrum, whose slope is commonly used to estimate the Hurst parameter of long–range dependence. We show that much more than simple slope estimates are needed for detecting important traffic features. In particular, the multi–scale nature of the traffic does not admit simple description of the type attempted by the Hurst parameter. By using simulated examples, we demonstrate the causes of a number of interesting effects in the wavelet spectrum of the data. This analysis leads us to a better understanding of several challenging phenomena observed in real network traffic. Although the wavelet analysis is robust to many smooth trends, high–frequency oscillations and non–stationarities such as abrupt changes in the mean have an important effect. In particular, the breaks and level–shifts in the local mean of the traffic rate can lead one to overestimate the Hurst parameter of the time series. Novel statistical techniques are required to address such issues in practice.