A multifractal wavelet model for positive processes

In this paper, we describe a new multiscale model for characterizing positive-valued and long-range dependent data. The model uses the Haar wavelet transform and puts a constraint on the wavelet coefficients to guarantee positivity, which results in a swift O(N) algorithm to synthesize N-point data sets. We elucidate our model´s ability to capture the covariance structure of real data, study its multifractal properties, and derive a scheme for matching it to real data observations. We demonstrate the model´s utility by applying it to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close match to the real data statistics (variance-time plots) and queuing behaviour