Multivariate wavelet Whittle estimation in long-range dependence

TL;DR

This paper introduces a wavelet-based semiparametric method for estimating long-range dependence and covariance in multivariate time series, effectively addressing phase-shift biases in real data applications across various fields.

Contribution

It proposes a novel multivariate wavelet Whittle estimator that is consistent for both stationary and nonstationary processes, improving correlation estimation accuracy.

Findings

Estimator is consistent for long-range dependence and covariance

Performs well in simulations and real data examples

Addresses phase-shift bias in correlation estimation

Abstract

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.