Cohen, E. A. K.; Gibberd, A. J. Wavelet spectra for multivariate point processes. (English) Zbl 07582655 Biometrika 109, No. 3, 837-851 (2022). Summary: Wavelets provide the flexibility for analysing stochastic processes at different scales. In this article we apply them to multivariate point processes as a means of detecting and analysing unknown nonstationarity, both within and across component processes. To provide statistical tractability, a temporally smoothed wavelet periodogram is developed and shown to be equivalent to a multi-wavelet periodogram. Under a stationarity 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 methods are applied to neural spike-train data, where it is shown to detect and characterize time-varying dependency patterns. MSC: 62-XX Statistics Keywords:coherence; point process; spectrum; stationarity test; wavelet PDFBibTeX XMLCite \textit{E. A. K. Cohen} and \textit{A. J. Gibberd}, Biometrika 109, No. 3, 837--851 (2022; Zbl 07582655) Full Text: DOI arXiv