Hurst multimodality detection based on large wavelet random matrices

Oliver Orejola (1) , Gustavo Didier (1) , Patrice Abry (2) , Herwig Wendt (3, 4)

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

In the modern world, systems are routinely monitored by multiple sensors, generating "Big Data" in the form of a large collection of time series. In this paper, we put forward a statistical methodology for detecting multimodality in the distribution of Hurst exponents in high-dimensional fractal systems. The methodology relies on the analysis of the distribution of the log-eigenvalues of large wavelet random matrices. Depending on the presence of a single or many Hurst exponents, we show that the wavelet empirical log-spectral distribution displays one or many modes, respectively, in the threefold limit as dimension, sample size and scale go to infinity. This allows for the construction of a unimodality test for the Hurst exponent distribution. Monte Carlo simulations show that the proposed methodology attains satisfactory power for realistic sample sizes.

Keywords: self-similarity; operator fractional Brownian motion; wavelets; random matrices; high dimensions; self-similarity

Domains: Computer Science [cs]

Oliver Orejola, Gustavo Didier, Patrice Abry, Herwig Wendt. Hurst multimodality detection based on large wavelet random matrices. 30th European Conference on Signal Processing (EUSIPCO 2022), European Association for Signal Processing (EURASIP), Aug 2022, Belgrade, Serbia. pp.2131-2135. ⟨hal-03850437v2⟩