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Bayesian estimation for the local assessment of the multifractality parameter of multivariate time series

Combrexelle, Sébastien and Wendt, Herwig and Altmann, Yoann and Tourneret, Jean-Yves and Mclaughlin, Stephen and Abry, Patrice Bayesian estimation for the local assessment of the multifractality parameter of multivariate time series. (2016) In: 24th European Signal Processing Conference (EUSIPCO 2016), 29 August 2016 - 2 September 2016 (Budapest, Hungary).

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Official URL: http://dx.doi.org/10.1109/EUSIPCO.2016.7760502

Abstract

Multifractal analysis (MF) is a widely used signal processing tool that enables the study of scale invariance models. Classical MF assumes homogeneous MF properties, which cannot always be guaranteed in practice. Yet, the local estimation of MF parameters has barely been considered due to the challenging statistical nature of MF processes (non-Gaussian, intricate dependence), requiring large sample sizes. This present work addresses this limitation and proposes a Bayesian estimator for local MF parameters of multivariate time series. The proposed Bayesian model builds on a recently introduced statistical model for leaders (i.e., specific multiresolution quantities designed for MF analysis purposes) that enabled the Bayesian estimation of MF parameters and extends it to multivariate non-overlapping time windows. It is formulated using spatially smoothing gamma Markov random field priors that counteract the large statistical variability of estimates for short time windows. Numerical simulations demonstrate that the proposed algorithm significantly outperforms current state-of-the-art estimators.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org This papers appears in Proceedings of EUSIPCO 2016 Electronic ISBN: 978-0-9928-6265-7 Electronic ISSN: 2076-1465 The original PDF of the article can be found at: http://ieeexplore.ieee.org/document/7760502/ Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-01447356
Audience (conference):International conference proceedings
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 > Heriot-Watt University (UNITED KINGDOM)
Laboratory name:
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Deposited By: IRIT IRIT
Deposited On:19 Jan 2017 13:26

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