Intermittent process analysis with scattering moments

Joan Bruna Estrach, S. Téphane Mallat, Emmanuel Bacry, Jean F Rançois Muzy

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)323-351
Number of pages29
JournalAnnals of Statistics
Volume43
Issue number1
DOIs
StatePublished - Feb 1 2015

Fingerprint

Scattering
Moment
Financial Time Series
Nonparametric Model
Intermittency
Fractional Brownian Motion
Energy Dissipation
Self-similarity
Random process
Poisson process
Expected Value
Turbulent Flow
Wavelet Transform
Increment
Random walk
Modulus
Random variable
Process analysis
Nonlinearity
Decay

Keywords

  • Generalized method of moments
  • Intermittency
  • Multifractal
  • Spectral analysis
  • Wavelet analysis

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Bruna Estrach, J., Mallat, S. T., Bacry, E., & Muzy, J. F. R. (2015). Intermittent process analysis with scattering moments. Annals of Statistics, 43(1), 323-351. https://doi.org/10.1214/14-AOS1276

Intermittent process analysis with scattering moments. / Bruna Estrach, Joan; Mallat, S. Téphane; Bacry, Emmanuel; Muzy, Jean F Rançois.

In: Annals of Statistics, Vol. 43, No. 1, 01.02.2015, p. 323-351.

Research output: Contribution to journalArticle

Bruna Estrach, J, Mallat, ST, Bacry, E & Muzy, JFR 2015, 'Intermittent process analysis with scattering moments', Annals of Statistics, vol. 43, no. 1, pp. 323-351. https://doi.org/10.1214/14-AOS1276
Bruna Estrach J, Mallat ST, Bacry E, Muzy JFR. Intermittent process analysis with scattering moments. Annals of Statistics. 2015 Feb 1;43(1):323-351. https://doi.org/10.1214/14-AOS1276
Bruna Estrach, Joan ; Mallat, S. Téphane ; Bacry, Emmanuel ; Muzy, Jean F Rançois. / Intermittent process analysis with scattering moments. In: Annals of Statistics. 2015 ; Vol. 43, No. 1. pp. 323-351.
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