ON MULTIVARIATE NON-GAUSSIAN SCALE INVARIANCE: FRACTIONAL LÉVY PROCESSES AND WAVELET ESTIMATION

B Cooper Boniece , Gustavo Didier (1) , Herwig Wendt (2, 3) , Patrice Abry (4)

1 Tulane University
2 IRIT-MINDS - CoMputational imagINg anD viSion
3 CNRS - Centre National de la Recherche Scientifique
4 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

In the modern world of "Big Data," dynamic signals are often multivariate and characterized by joint scale-free dynamics (self-similarity) and non-Gaussianity. In this paper, we examine the performance of joint wavelet eigenanalysis estimation for the Hurst parameters (scaling exponents) of non-Gaussian multivariate processes. We propose a new process called operator fractional Lévy motion (ofLm) as a Lévy-type model for non-Gaussian multivariate self-similarity. Based on large size Monte Carlo simulations of bivariate ofLm with a combination of Gaussian and non-Gaussian marginals, the estimation performance for Hurst parameters is shown to be satisfactory over finite samples.

Mots clés: multivariate self-similarity; non-Gaussian process; Lévy processes; wavelets

Domaines: Informatique [cs]; Traitement du signal et de l'image [eess.SP]

B Cooper Boniece, Gustavo Didier, Herwig Wendt, Patrice Abry. ON MULTIVARIATE NON-GAUSSIAN SCALE INVARIANCE: FRACTIONAL LÉVY PROCESSES AND WAVELET ESTIMATION. European Signal Processing Conference (EUSIPCO), Sep 2019, A Coruna, Spain. ⟨hal-02361748⟩