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Wavelet spectra for multivariate point processes
[The spectral analysis of point processes]

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  • E A K Cohen
  • A J Gibberd

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.

Suggested Citation

  • E A K Cohen & A J Gibberd, 2022. "Wavelet spectra for multivariate point processes [The spectral analysis of point processes]," Biometrika, Biometrika Trust, vol. 109(3), pages 837-851.
    • Handle: RePEc:oup:biomet:v:109:y:2022:i:3:p:837-851.
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    File URL: http://hdl.handle.net/10.1093/biomet/asab054
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    References listed on IDEAS

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