Effect of non-stationarities on multifractal analysis

Abstract

Multifractal analysis is concerned with the local scaling behavior of fractal processes such as those found in computer networks. Central to multifractal theory is the structure function tau(q) which links the power-law behavior of the moments of the process with its singularities through the multifractal formalism. Modern computer network traffic often contains non-stationarities such as shifts in the mean, periodicities, discontinuities, and polynomial trends due to human behavior and network protocols. In this paper, we determine the effect of these non-stationarities on the estimation of tau(q). Toward this end, numerical experiments were performed on the canonical multifractal process - the binomial cascade, which has been widely used to model wide area network traffic. Several time domain and wavelet domain estimators are evaluated in terms of their accuracy and robustness towards non-stationarities. It is found that time domain estimators are sensitive to non-stationarities whereas wavelet domain estimators are robust to all the non-stationarities considered at the expense of less accuracy