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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, 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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Contributor : Jean-François Muzy Connect in order to contact the contributor
Submitted on : Saturday, April 2, 2016 - 2:48:13 PM
Last modification on : Wednesday, January 12, 2022 - 3:37:24 AM

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Jean-François Muzy, Emmanuel Bacry, Stéphane Mallat, Joan Bruna. Intermittent process analysis with scattering moments. Annals of Statistics, Institute of Mathematical Statistics, 2015, 43 (1), pp.323. ⟨10.1214/14-AOS1276⟩. ⟨hal-01297107⟩



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