Multivariate scale-free dynamics: Testing fractal connectivity
Sébastien Combrexelle, Herwig Wendt, Gustavo Didier, Patrice Abry
Abstract
Scale-free dynamics commonly appear in individual components of multivariate data. Yet, while the behavior of cross-components is crucial in modeling real-world multivariate data, their examination often suggests departures from exact multivariate self-similarity (also termed fractal connectivity). The present paper introduces a multivariate Gaussian stochastic process with Hadamard (i.e., entry-wise) self-similar scale-free dynamics, controlled by a matrix Hurst parameter H, that allows departures from fractal connectivity. The properties of its wavelet coefficients and wavelet spectrum are studied, enabling the estimation of H and of the fractal connectivity parameter. Furthermore, it permits the computation of closed-form confidence intervals for the estimates based on approximate (wavelet) covariances. Finally, these developments enable us to devise a test for fractal connectivity. Monte Carlo simulations are used to assess the accuracy of the proposed approximate confidence intervals and the performance of the fractal connectivity test.
BibTeX
@inproceedings{icassp2017_multivariatescal,
title = {Multivariate scale-free dynamics: Testing fractal connectivity},
author = {Sébastien Combrexelle and Herwig Wendt and Gustavo Didier and Patrice Abry},
booktitle = {ICASSP 2017},
year = {2017}
}