Bootstrap for Empirical Multifractal Analysis

Abstract

Multifractal analysis is becoming a standard statistical analysis technique. In signal processing, it mostly consists of estimating scaling exponents characterizing scale invariance properties. For practical purposes, confidence intervals in estimation and p values in hypothesis testing are of primary importance. In empirical multifractal analysis, the statistical performance of estimation or test procedures remain beyond analytical derivation because of the theoretically involved nature of multifractal processes. Therefore, the goal of this article is to show how non-parametric bootstrap approaches circumvent such limitations and yield procedures that exhibit satisfactory statistical performance and can hence be practically used on real-life data. Such tools are illustrated at work on the analysis of the multifractal properties of empirical hydrodynamic turbulence data.