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

Sebastien Combrexelle, Herwig Wendt, Yoann Altmann, Jean-Yves Tourneret, Stephen McLaughlin, P. Abry

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publication2016 24th European Signal Processing Conference (EUSIPCO)
PublisherIEEE
Pages1518-1522
Number of pages5
ISBN (Electronic)9780992862657
DOIs
Publication statusPublished - 1 Dec 2016
Event24th European Signal Processing Conference 2016 - Hilton Budapest, Budapest, Hungary
Duration: 29 Aug 20162 Sep 2016
Conference number: 24

Publication series

NameEuropean Signal Processing Conference (EUSIPCO)
PublisherIEEE
ISSN (Print)2076-1465

Conference

Conference24th European Signal Processing Conference 2016
Abbreviated titleEUSIPCO 2016
CountryHungary
CityBudapest
Period29/08/162/09/16

Fingerprint

Time series
Invariance
Signal processing
Computer simulation
Statistical Models

Keywords

  • Bayesian estimation
  • GMRF
  • Multifractal analysis
  • Multivariate time series
  • Whittle likelihood

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Combrexelle, S., Wendt, H., Altmann, Y., Tourneret, J-Y., McLaughlin, S., & Abry, P. (2016). Bayesian estimation for the local assessment of the multifractality parameter of multivariate time series. In 2016 24th European Signal Processing Conference (EUSIPCO) (pp. 1518-1522). (European Signal Processing Conference (EUSIPCO)). IEEE. https://doi.org/10.1109/EUSIPCO.2016.7760502
Combrexelle, Sebastien ; Wendt, Herwig ; Altmann, Yoann ; Tourneret, Jean-Yves ; McLaughlin, Stephen ; Abry, P. / Bayesian estimation for the local assessment of the multifractality parameter of multivariate time series. 2016 24th European Signal Processing Conference (EUSIPCO). IEEE, 2016. pp. 1518-1522 (European Signal Processing Conference (EUSIPCO)).
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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.",
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Combrexelle, S, Wendt, H, Altmann, Y, Tourneret, J-Y, McLaughlin, S & Abry, P 2016, Bayesian estimation for the local assessment of the multifractality parameter of multivariate time series. in 2016 24th European Signal Processing Conference (EUSIPCO). European Signal Processing Conference (EUSIPCO), IEEE, pp. 1518-1522, 24th European Signal Processing Conference 2016, Budapest, Hungary, 29/08/16. https://doi.org/10.1109/EUSIPCO.2016.7760502

Bayesian estimation for the local assessment of the multifractality parameter of multivariate time series. / Combrexelle, Sebastien; Wendt, Herwig; Altmann, Yoann; Tourneret, Jean-Yves; McLaughlin, Stephen; Abry, P.

2016 24th European Signal Processing Conference (EUSIPCO). IEEE, 2016. p. 1518-1522 (European Signal Processing Conference (EUSIPCO)).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - 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.

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Combrexelle S, Wendt H, Altmann Y, Tourneret J-Y, McLaughlin S, Abry P. Bayesian estimation for the local assessment of the multifractality parameter of multivariate time series. In 2016 24th European Signal Processing Conference (EUSIPCO). IEEE. 2016. p. 1518-1522. (European Signal Processing Conference (EUSIPCO)). https://doi.org/10.1109/EUSIPCO.2016.7760502