A statistical analysis of morse wavelet coherence
IEEE Transactions on Signal Processing
Transient Detection With Cross Wavelet Transforms and Wavelet Coherence
IEEE Transactions on Signal Processing
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
Multivariate generalized Laplace distribution and related random fields
Journal of Multivariate Analysis
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The use of the wavelet coherence of two series in hypothesis testing relies on some sort of smoothing being carried out in order that the coherence estimator is not simply unity. A previous study considered averaging via the use of multiple Morse wavelets. Here we consider time-domain smoothing and use of a single Morlet wavelet. Since the Morlet wavelet is complex-valued,we derive analytic results for the case of wavelet coherence calculated from complex-valued, jointly stationary and Gaussian time series. The temporally smoothed wavelet coherence can be written in terms of Welch's overlapping segment averaging (WOSA) spectrum estimators, and by using multitaper equivalent representations for the WOSA estimators we show that Goodman's distribution is appropriate asymptotically, and readily derive the appropriate degrees of freedom. The theoretical results are verified via simulations and illustrated using solar physics data.