Multivariate Scale-free dynamics: Testing Fractal Connectivity

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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  • HAL Id : hal-01912795, version 1
  • OATAO : 19136

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Sébastien Combrexelle, Herwig Wendt, Gustavo Didier, Patrice Abry. Multivariate Scale-free dynamics: Testing Fractal Connectivity. 42nd IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2017), Mar 2017, New Orleans, United States. pp.3984-3988. ⟨hal-01912795⟩

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