Multivariate scale-free dynamics: Testing fractal connectivity
Authors: 
S. Combrexelle, H. Wendt, G. Didier, P. AbryAuthors Info & Claims
Pages 3984 - 3988
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.
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Published: 05 March 2017
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