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February 2015 Intermittent process analysis with scattering moments
Joan Bruna, Stéphane Mallat, Emmanuel Bacry, Jean-François Muzy
Ann. Statist. 43(1): 323-351 (February 2015). DOI: 10.1214/14-AOS1276

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, Lévy 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.

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Joan Bruna. Stéphane Mallat. Emmanuel Bacry. Jean-François Muzy. "Intermittent process analysis with scattering moments." Ann. Statist. 43 (1) 323 - 351, February 2015. https://doi.org/10.1214/14-AOS1276

Information

Published: February 2015
First available in Project Euclid: 6 February 2015

zbMATH: 1308.62168
MathSciNet: MR3311862
Digital Object Identifier: 10.1214/14-AOS1276

Subjects:
Primary: 62M10, 62M15, 62M40

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 1 • February 2015
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