Wavelet spectra for multivariate point processes

The spectral analysis of point processes

E A K Cohen and A J Gibberd

Biometrika, 2022, vol. 109, issue 3, 837-851

Abstract: SummaryWavelets provide the flexibility for analysing stochastic processes at different scales. In this article we apply them to multivariate point processes as a means of detecting and analysing unknown nonstationarity, both within and across component processes. To provide statistical tractability, a temporally smoothed wavelet periodogram is developed and shown to be equivalent to a multi-wavelet periodogram. Under a stationarity 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 methods are applied to neural spike-train data, where it is shown to detect and characterize time-varying dependency patterns.

Keywords: Coherence; Point process; Spectrum; Stationarity test; Wavelet (search for similar items in EconPapers)
Date: 2022
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