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, 2021,109 : 837-851, https://doi.org/10.1093/biomet/asab054 is available online at: https://academic.oup.com/biomet/article/109/3/837/6415823
Accepted author manuscript, 1.68 MB, PDF document
Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Wavelet Spectra for Multivariate Point Processes
AU - Cohen, Edward
AU - Gibberd, Alex
N1 - 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, 2021,109 : 837-851, https://doi.org/10.1093/biomet/asab054 is available online at: https://academic.oup.com/biomet/article/109/3/837/6415823
PY - 2022/9/30
Y1 - 2022/9/30
N2 - 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.
AB - 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.
KW - wavelet
KW - spectra
KW - time-series
KW - point process
U2 - 10.1093/biomet/asab054
DO - 10.1093/biomet/asab054
M3 - Journal article
VL - 109
SP - 837
EP - 851
JO - Biometrika
JF - Biometrika
SN - 0006-3444
IS - 3
ER -