  Wavelets provide the flexibility to analyse stochastic processes at different
scales. Here, we apply them to multivariate point processes as a means of
detecting and analysing unknown non-stationarity, both within and across data
streams. To provide statistical tractability, a temporally smoothed wavelet
periodogram is developed and shown to be equivalent to a multi-wavelet
periodogram. Under a stationary assumption, the distribution of the temporally
smoothed wavelet periodogram is demonstrated to be asymptotically Wishart, with
the centrality matrix and degrees of freedom readily computable from the
multi-wavelet formulation. Distributional results extend to wavelet coherence;
a time-scale measure of inter-process correlation. This statistical framework
is used to construct a test for stationarity in multivariate point-processes.
The methodology is applied to neural spike train data, where it is shown to
detect and characterise time-varying dependency patterns.
