Time-Scale Block Bootstrap Tests for Non Gaussian Finite Variance Self-Similar Processes with Stationary Increments

摘要

Scaling analysis is nowadays becoming a standard tool in statistical signal processing. It mostly consists of estimating scaling attributes which in turns are involved in standard tasks such as detection, identification or classification. Recently, we proposed that confidence interval or hypothesis test design for scaling analysis could be based on non parametric bootstrap approaches. We showed that such procedures are efficient to decide whether data are better modeled with Gaussian fractional Brownian motion or with multifractal processes. In the present contribution, we investigate the relevance of such bootstrap procedures to discriminate between non Gaussian finite variance self similar processes with stationary increments (such as Rosenblatt process) and multifractal processes. To do so, we introduce a new joint time-scale block based bootstrap scheme and make use of the most recent scaling analysis tools, based on wavelet leaders.