Wavelet spectra for multivariate point processes
File(s)
Published version
Author(s)
Cohen, Edward
Gibberd, Alexander
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.
Date Issued
2022-09
Date Acceptance
2021-10-13
Citation
Biometrika, 2022, 109 (3), pp.837-851
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.
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.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://academic.oup.com/biomet/advance-article/doi/10.1093/biomet/asab054/6415823
Grant Number
EP/P011535/1
Subjects
0103 Numerical and Computational Mathematics
0104 Statistics
1403 Econometrics
Statistics & Probability
Publication Status
Published
Date Publish Online
2021-11-03