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Wavelet spectra for multivariate point processes

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Title: Wavelet spectra for multivariate point processes
Authors: Cohen, E
Gibberd, A
Item Type: Journal Article
Abstract: 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 characterize time-varying dependency patterns.
Issue Date: Sep-2022
Date of Acceptance: 13-Oct-2021
URI: http://hdl.handle.net/10044/1/92710
DOI: 10.1093/biomet/asab054
ISSN: 0006-3444
Publisher: Oxford University Press
Start Page: 837
End Page: 851
Journal / Book Title: Biometrika
Volume: 109
Issue: 3
Copyright Statement: © 2021 Biometrika Trust This is an Open Access article distributed under the terms of the Creative CommonsAttribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/P011535/1
Keywords: 0103 Numerical and Computational Mathematics
0104 Statistics
1403 Econometrics
Statistics & Probability
Publication Status: Published
Open Access location: https://academic.oup.com/biomet/advance-article/doi/10.1093/biomet/asab054/6415823?guestAccessKey=57a74eab-6635-4fb5-b2ab-79713b658925
Online Publication Date: 2021-11-03
Appears in Collections:Statistics
Faculty of Natural Sciences

This item is licensed under a Creative Commons License Creative Commons