The Annals of Statistics
- Ann. Statist.
- Volume 43, Number 1 (2015), 323-351.
Intermittent process analysis with scattering moments
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.
Ann. Statist., Volume 43, Number 1 (2015), 323-351.
First available in Project Euclid: 6 February 2015
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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
- Supplementary material: Proofs of theorems. We provide the technical derivations of all the results.