A statistical analysis of morse wavelet coherence

Authors:
Ed A. K. Cohen;Andrew T. Walden
Affiliations:
Department of Mathematics, Imperial College London, London, U.K.;Department of Mathematics, Imperial College London, London, U.K.
Venue:
IEEE Transactions on Signal Processing
Year:
2010

Citing 6
Cited 1

Generalized Morse wavelets

IEEE Transactions on Signal Processing
Second-order statistics of complex signals

IEEE Transactions on Signal Processing
Transient Detection With Cross Wavelet Transforms and Wavelet Coherence

IEEE Transactions on Signal Processing
Second-order analysis of improper complex random vectors and processes

IEEE Transactions on Signal Processing
Simulation of Improper Complex-Valued Sequences

IEEE Transactions on Signal Processing
Kinematics of Complex-Valued Time Series

IEEE Transactions on Signal Processing

A statistical study of temporally smoothed wavelet coherence

IEEE Transactions on Signal Processing

Quantified Score

Hi-index	35.69

Visualization

Abstract

Wavelet coherence computed from two time series has been widely applied in hypothesis testing situations, but has proven resistant to analytic study, with resort to simulations for statistical properties. As part of the null hypothesis being tested, such simulations invariably assume joint stationarity of the series. If estimated using multiple orthogonal Morse wavelets, wavelet coherence is in fact amenable to statistical study. Since the wavelets are complex-valued, we consider the case of wavelet coherence calculated from discrete-time complex-valued and stationary time series. Under Gaussianity, the Goodman distribution is, for large samples, appropriate for wavelet coherence. The true wavelet coherence value is identified in terms of its frequency domain equivalent. Theoretical results are illustrated and verified via simulations.