## The Annals of Statistics

### 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.

#### Article information

Source
Ann. Statist., Volume 43, Number 1 (2015), 323-351.

Dates
First available in Project Euclid: 6 February 2015

https://projecteuclid.org/euclid.aos/1423230082

Digital Object Identifier
doi:10.1214/14-AOS1276

Mathematical Reviews number (MathSciNet)
MR3311862

Zentralblatt MATH identifier
1308.62168

#### Citation

Bruna, Joan; Mallat, Stéphane; Bacry, Emmanuel; Muzy, Jean-François. Intermittent process analysis with scattering moments. Ann. Statist. 43 (2015), no. 1, 323--351. doi:10.1214/14-AOS1276. https://projecteuclid.org/euclid.aos/1423230082

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