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

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.