Estimating Time-Evolving Partial Coherence between Signals via Multivariate Locally Stationary Wavelet Processes

Timothy Park, Idris A. Eckley, Hernando C. Ombao

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


We consider the problem of estimating time-localized cross-dependence in a collection of nonstationary signals. To this end, we develop the multivariate locally stationary wavelet framework, which provides a time-scale decomposition of the signals and, thus, naturally captures the time-evolving scale-specific cross-dependence between components of the signals. Under the proposed model, we rigorously define and estimate two forms of cross-dependence measures: wavelet coherence and wavelet partial coherence. These dependence measures differ in a subtle but important way. The former is a broad measure of dependence, which may include indirect associations, i.e., dependence between a pair of signals that is driven by another signal. Conversely, wavelet partial coherence measures direct linear association between a pair of signals, i.e., it removes the linear effect of other observed signals. Our time-scale wavelet partial coherence estimation scheme thus provides a mechanism for identifying hidden dynamic relationships within a network of nonstationary signals, as we demonstrate on electroencephalograms recorded in a visual-motor experiment.

Original languageEnglish (US)
Article number6868283
Pages (from-to)5240-5250
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number20
StatePublished - Oct 15 2014


  • Coherence
  • local stationarity
  • multivariate signals
  • partial coherence
  • wavelets

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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