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Multivariate Wavelet Whittle Estimation in Long‐range Dependence
Author(s) -
Achard Sophie,
Gannaz Irène
Publication year - 2016
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12170
Subject(s) - multivariate statistics , autocorrelation , covariance matrix , range (aeronautics) , mathematics , wavelet , covariance , series (stratigraphy) , matrix (chemical analysis) , estimation of covariance matrices , econometrics , statistical physics , statistics , algorithm , computer science , artificial intelligence , paleontology , physics , materials science , composite material , biology
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 owing 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.