Wavelet Coherence for Certain Nonstationary Bivariate Processes

A previous study considered the estimation of wavelet coherence from jointly stationary time series via time-domain smoothing and use of a single Morlet wavelet. The form of the asymptotic (Goodman's) distribution was derived. In this paper we extend this approach to nonstationary time series where the nonstationarity is induced by various types of modulation. The model forms of coherence studied include constant over time and scale, time-varying, scale-varying, and time-and-scale varying. These coherence models are carefully derived from appropriate statistical models for nonstationary processes. The portion of the signals used in calculating the coherence at a scale a depends on a; provided its size-or equivalently the number of degrees of freedom of the estimator-is appropriate to the time variation in coherence at that scale, good estimation results are achieved. Moreover, Goodman's distribution is seen still to be appropriate for the estimator.