Time-Dependent Dual-Frequency Coherence in Multivariate Non-Stationary Time Series

Cristina Gorrostieta, Hernando Ombao, Rainer Von Sachs

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Coherence is one common metric for cross-dependence in multichannel signals. However, standard coherence does not sufficiently model many biological signals with complex dependence structures such as cross-oscillatory interactions between a low-frequency component in one signal and a high-frequency component in another. The notion of cross-dependence between low- and high-frequency components, as defined in classical harmonizable processes, is still inadequate because it assumes time invariance and thus cannot capture cross-frequency interactions that evolve over time. We construct a novel framework for modeling and estimating these dependencies under the replicated time series setting. Under this framework, we establish the novel concept of evolutionary dual-frequency coherence and develop time-localized estimators based on dual-frequency local periodograms. The proposed nonparametric estimation procedure does not suffer from model misspecification. It uses the localized fast Fourier transform and hence is able to handle massive data. When applied to electroencephalogram data recorded in a motor intention experiment, the proposed method uncovers new and interesting cross-oscillatory interactions that have been overlooked by the standard approaches.
Original languageEnglish (US)
Pages (from-to)3-22
Number of pages20
JournalJournal of Time Series Analysis
Issue number1
StatePublished - Jul 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank two anonymous referees and the associate editor for helpful comments, which helped improve the presentation of our paper. HO acknowledges funding support from the US National Science Foundation Division of Mathematical Sciences. RvS gratefully acknowledges funding by the contract ‘Projet d'Actions de Recherche Concertées' No. 12/17-045 of the ‘Communauté française de Belgique’ and by IAP research network Grant P7/06 of the Belgian government (Belgian Science Policy).


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