Home > Research > Publications & Outputs > Wavelet Spectra for Multivariate Point Processes

Electronic data

  • wsmvpp_no_formatting

    Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated versionE A K Cohen, A J Gibberd, Wavelet Spectra for Multivariate Point Processes, Biometrika, 2021;, asab054, https://doi.org/10.1093/biomet/asab054 is available online at:

    Accepted author manuscript, 1.68 MB, PDF document

    Embargo ends: 2/11/22

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Text available via DOI:

View graph of relations

Wavelet Spectra for Multivariate Point Processes

Research output: Contribution to journalJournal articlepeer-review

E-pub ahead of print
<mark>Journal publication date</mark>2/11/2021
<mark>Journal</mark>Biometrika
Publication StatusE-pub ahead of print
Early online date2/11/21
<mark>Original language</mark>English

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.

Bibliographic note

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated versionE A K Cohen, A J Gibberd, Wavelet Spectra for Multivariate Point Processes, Biometrika, 2021;, asab054, https://doi.org/10.1093/biomet/asab054 is available online at: