Wavelet Spectra for Multivariate Point Processes
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 characterise time-varying dependency patterns.
Cite
@article{arxiv.1908.02634,
title = {Wavelet Spectra for Multivariate Point Processes},
author = {Edward A. K. Cohen and Alexander J. Gibberd},
journal= {arXiv preprint arXiv:1908.02634},
year = {2020}
}