Multivariate wavelet Whittle estimation in long-range dependence

Sophie Achard (1, 2, 3, 4) , Irène Gannaz (5, 6, 7)

1 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing
2 CNRS - Centre National de la Recherche Scientifique
3 UGA [2016-2019] - Université Grenoble Alpes [2016-2019]
4 GIN - [GIN] Grenoble Institut des Neurosciences
5 ICJ - Institut Camille Jordan
6 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
7 PSPM - Probabilités, statistique, physique mathématique

Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual estimations of correlation can be highly biased due to phase-shifts caused by the differences in the properties of autocorrelation in the processes. To address this issue, we introduce a 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, also called functional connectivity in neuroscience. This matrix characterizes coupling between time series. 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 and to encompass both stationary and nonstationary processes. A simulation study and a real data example are presented to illustrate the finite sample behaviour.

Mots clés: functional connectivity; multivariate processes; long memory; fractional integration; semiparametric estimation; covariance matrix; wavelets; neuroscience application

Domaines: Statistiques [math.ST]

Sophie Achard, Irène Gannaz. Multivariate wavelet Whittle estimation in long-range dependence. Journal of Time Series Analysis, 2016, 37 (4), pp.476-512. ⟨10.1111/jtsa.12170⟩. ⟨hal-01079645v2⟩