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Pré-Publication, Document De Travail Année : 2014

Multivariate wavelet Whittle estimation in long-range dependence

Résumé

This paper deals with the semiparametric estimation of multivariate long-range dependent processes. The parameters of interest in the model are the vector of the long-range dependence parameters and the long-run covariance matrix. The proposed multivariate wavelet-based Whittle estimation is shown to be consistent for the estimation of both the long-range dependence and the covariance matrix. A simulation study confirms the satisfying behaviour of the estimation, which improves the univariate estimation and gives similar results than multivariate Fourier-based procedure. For real data applications, the correlation between time series is an important feature. Usual estimations can be highly biased due to phase-shifts caused by the differences in the properties of autocorrelation in the processes. The long-run covariance matrix provides an interesting estimator for characterizing coupling between time series, also called functional connectivity in neuroscience. A real data application in neuroscience highlights the utility of the wavelets-based method, which is more flexible than Fourier-based procedures. Time series measuring the brain activity are analysed, so as to obtain the characterization of their long-memory behaviour and a measure of the functional connectivity of the brain.
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Dates et versions

hal-01079645 , version 1 (03-11-2014)
hal-01079645 , version 2 (30-10-2015)

Identifiants

  • HAL Id : hal-01079645 , version 1

Citer

Sophie Achard, Irène Gannaz. Multivariate wavelet Whittle estimation in long-range dependence. 2014. ⟨hal-01079645v1⟩

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