Intermittent process analysis with scattering moments

By Joan Bruna, Stéphane Mallat, Emmanuel Bacry, Jean-François Muzy. 2013

65 citations recorded by the source corpus.

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, L\'{e}vy 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.

Subfields: Economics and Econometrics, Finance

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Citations in the corpus

Invariant Risk Minimization (2019, background): “Unfortunately, spurious correlations and biases are often simpler to detect than the true phenomenon of interest [17, 9, 10, 11].”
Understanding deep convolutional networks (2016, background): “One can prove that scattering moments characterize complex multiscale properties of fractals and multifractal processes, such as Brownian motions, Levi processes or Mandelbrot cascades [7].”
Wavelet Scattering Regression of Quantum Chemical Energies (2016, background): “This type of coupling property was also observed for multifractal stochastic processes in [12].”
Rigid-Motion Scattering for Texture Classification (2014, background): “Translation invariant scattering representation of stationary processes have been studied to discriminate texture which do not involve important rotation or scaling variability [7, 11].”
A Mathematical Motivation for Complex-Valued Convolutional Networks (2015, background): “Further information is available in the original work of Daubechies (1992), Meyer (1993), Coifman, Meyer, Quake, and Wickerhauser (1994), Coifman and Donoho (1995), Simoncelli and Freeman (1995), Meyer and Coifman (1997), LeCun, Bottou, Bengio, and Haffner (1998), Donoho, Mallat, von Sachs, and Samu”
Kymatio: Scattering Transforms in Python (2018, background): “It has many favorable theoretical properties (Mallat, 2012; Bruna et al., 2015; Waldspurger, 2017) and enjoys considerable success as a powerful tool in modern signal processing (Adel et al., 2017; Bruna and Mallat, 2013; And´en and Mallat, 2014; Chud´aˇcek et al., 2014; Sifre and Mallat, 2013;…”