Scale Dependencies and SelfSimilar Models with Wavelet Scattering Spectra
Abstract
We introduce the wavelet scattering spectra which provide nonGaussian models of timeseries having stationary increments. A complex wavelet transform computes signal variations at each scale. Dependencies across scales are captured by the joint correlation across time and scales of wavelet coefficients and their modulus. This correlation matrix is nearly diagonalized by a second wavelet transform, which defines the scattering spectra. We show that this vector of moments characterizes a wide range of nonGaussian properties of multiscale processes. We prove that selfsimilar processes have scattering spectra which are scale invariant. This property can be tested statistically on a single realization and defines a class of widesense selfsimilar processes. We build maximum entropy models conditioned by scattering spectra coefficients, and generate new timeseries with a microcanonical sampling algorithm. Applications are shown for highly nonGaussian financial and turbulence timeseries.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 DOI:
 10.48550/arXiv.2204.10177
 arXiv:
 arXiv:2204.10177
 Bibcode:
 2022arXiv220410177M
 Keywords:

 Physics  Data Analysis;
 Statistics and Probability;
 Condensed Matter  Disordered Systems and Neural Networks;
 Computer Science  Machine Learning;
 Electrical Engineering and Systems Science  Signal Processing;
 Quantitative Finance  Mathematical Finance;
 Statistics  Machine Learning