Intermittent process analysis with scattering moments
Abstract
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, L\'{e}vy 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.
Cite
@article{arxiv.1311.4104,
title = {Intermittent process analysis with scattering moments},
author = {Joan Bruna and Stéphane Mallat and Emmanuel Bacry and Jean-François Muzy},
journal= {arXiv preprint arXiv:1311.4104},
year = {2015}
}
Comments
Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)