Multi-wavelet coherence for point processes on the real line

Coherence is a well established measure of linear dependency between a pair of stationary random processes in the frequency domain. Wavelet coherence measures the linear dependency between a pair of signals in time-scale space and is therefore more suitable for non-stationary processes. Until now it has only been considered in relation to regularly sampled ordinary time-series. Here, for the first time, it is applied to point processes on the real line. We consider smoothing the individual wavelet spectra by averaging over a set of orthogonal Morse wavelets and show that under the assumption of independent Poisson processes the Goodman distribution is appropriate.