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Multifractal Characterization for Bivariate Data

Leonarduzzi, Roberto and Abry, Patrice and Roux, Stéphane and Wendt, Herwig and Jaffard, Stéphane and Seuret, Stéphane Multifractal Characterization for Bivariate Data. (2018) In: 26th European Signal and Image Processing Conference (EUSIPCO 2018), 3 September 2018 - 7 September 2018 (Roma, Italy).

(Document in English)

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Official URL: https://doi.org/10.23919/EUSIPCO.2018.8553435


Multifractal analysis is a reference tool for the analysis of data based on local regularity, which has been proven useful in an increasing number of applications. However, in its current formulation, it remains a fundamentally univariate tool, while being confronted with multivariate data in an increasing number of applications. Recent contributions have explored a first multivariate theoretical grounding for multi fractal analysis and shown that it can be effective in capturing and quantifying transient higher-order dependence beyond correlation. Building on these first fundamental contributions, this work proposes and studies the use of a quadratic model for the joint multi fractal spectrum of bivariate time series. We obtain expressions for the Pearson correlation in terms of the random walk and a multifractal cascade dependence parameters under this model, provide complete expressions for the multifractal parameters and propose a transformation of these parameters into natural coordinates that allows to effectively summarize the information they convey. Finally, we propose estimators for these parameters and assess their statistical performance through numerical simulations. The results indicate that the bivariate multi fractal parameter estimates are accurate and effective in quantifying non-linear, higher-order dependencies between time series.

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 2018.Electronic ISBN: 978-9-0827-9701-5 Electronic ISSN: 2076-1465 The original PDF of the article can be found at: https://ieeexplore.ieee.org/document/8553435 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-02279400
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 - Toulouse INP (FRANCE)
Other partners > Université Paris Est Créteil Val de Marne - UPEC (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (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 > Université de Lyon - UDL (FRANCE)
Other partners > Université Paris-Est Marne-La-Vallée - UPEM (FRANCE)
Laboratory name:
ANR : Agence nationale de la recherche (France)
Deposited On:22 Jul 2019 13:56

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