INTERMITTENT PROCESS ANALYSIS WITH SCATTERING MOMENTS

• 成果类型: Article
• 署名作者: Bruna, Joan; Mallat, Stephane; Bacry, Emmanuel; Muzy, Jean-Francois
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1276
• 发表日期: 2015
• 页码: 323-351
• 关键词: multifractal formalism; fractal signals; wavelet leaders; transform; bootstrap; models

摘要

Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and modulus nonlinearities, which preserves the variance. First- and second-order scattering moments are shown to characterize intermittency and self-similarity properties of multiscale processes. Scattering moments of Poisson processes, fractional Brownian motions, Levy processes and multifractal random walks are shown to have characteristic decay. The Generalized Method of Simulated Moments is applied to scattering moments to estimate data generating models. Numerical applications are shown on financial time-series and on energy dissipation of turbulent flows.