Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 3, Pages 980-989Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2009.2033645
Keywords
Coherence; Goodman distribution; Morse wavelets; wavelet coherence
Categories
Funding
- EPSRC (U.K.)
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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.
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