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• W1591281844 abstract "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." @default.
• W1591281844 created "2016-06-24" @default.
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• W1591281844 date "2015-04-01" @default.
• W1591281844 modified "2023-10-14" @default.
• W1591281844 title "A Bayesian approach for the joint estimation of the multifractality parameter and integral scale based on the Whittle approximation" @default.
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• W1591281844 doi "https://doi.org/10.1109/icassp.2015.7178699" @default.
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