Wavelet spectra for multivariate point processes

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