Paper Info
Title
Bayesian estimation for the local assessment of the multifractality parameter of multivariate time series.
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.
Year
Venue
Keywords
2016
European Signal Processing Conference
Multifractal analysis,Bayesian estimation,Multivariate time series,Whittle likelihood,GMRF
Field
DocType
ISSN
Time series,Bayesian inference,Computer science,Markov random field,Algorithm,Smoothing,Statistical model,Prior probability,Statistics,Bayes estimator,Estimator
Conference
2076-1465
Citations 
PageRank 
References 
0
0.34
0
Authors
6
Name
Order
Citations
PageRank
Sébastien Combrexelle102.37
Herwig Wendt217033.82
Yoann Altmann322922.58
Jean-Yves Tourneret41154104.46
Stephen McLaughlin546443.14
Patrice Abry656763.81