{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T17:52:54Z","timestamp":1785520374540,"version":"3.56.0"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T00:00:00Z","timestamp":1635811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,8,24]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1093\/biomet\/asab054","type":"journal-article","created":{"date-parts":[[2021,10,27]],"date-time":"2021-10-27T19:12:03Z","timestamp":1635361923000},"page":"837-851","source":"Crossref","is-referenced-by-count":2,"title":["Wavelet spectra for multivariate point processes"],"prefix":"10.1093","volume":"109","author":[{"given":"E A K","family":"Cohen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Imperial College London, South Kensington Campus , London SW7 2AZ, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A J","family":"Gibberd","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Lancaster University , Bailrigg, Lancaster LA1 4YF, U.K"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,11,2]]},"reference":[{"key":"2022082420280413600_B1","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1111\/j.2517-6161.1963.tb00508.x","article-title":"The spectral analysis of point processes","volume":"25","author":"Bartlett,","year":"1963","journal-title":"J. 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