A BAYESIAN APPROACH FOR THE JOINT ESTIMATION OF THE MULTIFRACTALITY PARAMETER AND INTEGRAL SCALE BASED ON THE WHITTLE APPROXIMATION

被引:0
|
作者
Combrexelle, S. [1 ]
Wendt, H. [1 ]
Abry, P. [2 ]
Dobigeon, N. [1 ]
McLaughlin, S. [3 ]
Tourneret, J. -Y [1 ]
机构
[1] Univ Toulouse, CNRS, IRIT ENSEEIHT, F-31062 Toulouse, France
[2] Ecole Normale Super Lyon, Phys Dept, CNRS, F-69364 Lyon, France
[3] Heriot Watt Univ, Sch Engn & Phys Sci, Edinburgh, Midlothian, Scotland
来源
2015 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING (ICASSP) | 2015年
基金
英国工程与自然科学研究理事会;
关键词
Multifractal Analysis; Integral Scale; Wavelet Leaders; Bayesian Estimation; Whittle Likelihood; TURBULENT FLOWS; ASSET RETURNS; INTERMITTENCY; CASCADES;
D O I
暂无
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
Multifractal analysis is a powerful tool used in signal processing. Multifractal models are essentially characterized by two parameters, the multifractality parameter c(2) and the integral scale A (the time scale beyond which multifractal properties vanish). Yet, most applications concentrate on estimating c(2) while the estimation of A is in general overlooked, despite the fact that A potentially conveys important information. Joint estimation of c(2) and A is challenging due to the statistical nature of multifractal processes (i.e. the strong dependence and non-Gaussian nature), and has barely been considered. The present contribution addresses these limitations and proposes a Bayesian procedure for the joint estimation of (c(2), A). Its originality resides, first, in the construction of a generic multivariate model for the statistics of wavelet leaders for multifractal multiplicative cascade processes, and second, in the use of a suitable Whittle approximation for the likelihood associated with the model. The resulting model enables Bayesian estimators for (c(2), A) to also be computed for large sample size. Performance is assessed numerically for synthetic multifractal processes and illustrated for wind-tunnel turbulence data. The proposed procedure significantly improves estimation of c(2) and yields, for the first time, reliable estimates for A.
引用
收藏
页码:3886 / 3890
页数:5
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