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Multivariate Hadamard self-similarity: testing fractal connectivity

Wendt, Herwig and Didier, Gustavo and Combrexelle, Sébastien and Abry, Patrice Multivariate Hadamard self-similarity: testing fractal connectivity. (2017) Physica D: Nonlinear Phenomena, 356-357. 1-36. ISSN 0167-2789

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Official URL: https://doi.org/10.1016/j.physd.2017.07.001

Abstract

While scale invariance is commonly observed in each component of real world multivariate signals, it is also often the case that the inter-component correlation structure is not fractally connected, i.e., its scaling behavior is not determined by that of the individual components. To model this situation in a versatile manner, we introduce a class of multivariate Gaussian stochastic processes called Hadamard fractional Brownian motion (HfBm). Its theoretical study sheds light on the issues raised by the joint requirement of entry-wise scaling and departures from fractal connectivity. An asymptotically normal wavelet-based estimator for its scaling parameter, called the Hurst matrix, is proposed, as well as asymptotically valid confidence intervals. The latter are accompanied by original finite sample procedures for computing confidence intervals and testing fractal connectivity from one single and finite size observation. Monte Carlo simulation studies are used to assess the estimation performance as a function of the (finite) sample size, and to quantify the impact of omitting wavelet cross-correlation terms. The simulation studies are shown to validate the use of approximate confidence intervals, together with the significance level and power of the fractal connectivity test. The test performance and properties are further studied as functions of the HfBm parameters.

Item Type:Article
Additional Information:https://www.sciencedirect.com/science/article/pii/S0167278916306650
HAL Id:hal-02345555
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Normale Supérieure de Lyon - ENS de Lyon (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Other partners > Tulane University (USA)
Other partners > Université de Lyon - UDL (FRANCE)
Laboratory name:
Funders:
ANR : Agence nationale de la recherche (France) - ARO : Army Research Office (US)
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Deposited By: IRIT IRIT
Deposited On:04 Nov 2019 12:48

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