Intermittent process analysis with scattering moments

DOI10.1214/14-AOS1276zbMath1308.62168arXiv1311.4104MaRDI QIDQ2338929

Emmanuel Bacry, Joan Bruna, Stephane Mallat, Jean-François Muzy

Publication date: 27 March 2015

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.4104

zbMATH Keywords

wavelet analysisgeneralized method of momentsspectral analysisintermittencymultifractal

Mathematics Subject Classification ID

Random fields; image analysis (62M40) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Applications of statistics to actuarial sciences and financial mathematics (62P05) Nonparametric estimation (62G05) Inference from stochastic processes and spectral analysis (62M15)

Related Items

Asymptotic analysis of higher-order scattering transform of Gaussian processes ⋮ Static and dynamical, fractional uncertainty principles ⋮ Central and Noncentral Limit Theorems Arising from the Scattering Transform and Its Neural Activation Generalization ⋮ A Mathematical Motivation for Complex-Valued Convolutional Networks ⋮ Wavelet Scattering Regression of Quantum Chemical Energies ⋮ Multifractal Analysis of Multivariate Images Using Gamma Markov Random Field Priors ⋮ Multiscale sparse microcanonical models ⋮ Intermittent process analysis with scattering moments

Uses Software

• ScatNet
• Multifractal

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large Sample Properties of Generalized Method of Moments Estimators
• Continuous cascade models for asset returns
• Spectral estimation of the fractional order of a Lévy process
• Wavelet leaders and bootstrap for multifractal analysis of images
• Sur certaines martingales de Benoit Mandelbrot
• Singularity spectrum of fractal signals from wavelet analysis: Exact results
• Log-infinitely divisible multifractal processes
• Intermittent process analysis with scattering moments
• Introductory lectures on fluctuations of Lévy processes with applications.
• Group Invariant Scattering
• Multifractal Formalism for Functions Part I: Results Valid For All Functions
• Multifractal Formalism for Functions Part II: Self-Similar Functions
• Deep Scattering Spectrum
• A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration
• Log-normal continuous cascade model of asset returns: aggregation properties and estimation
• Wavelet methods for pointwise regularity and local oscillations of functions