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

Coherence is one common metric for cross-dependence in multichannel signals. However, standard coherence does not suf- ficiently 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.

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Document type	Article de périodique (Journal article) – Article de recherche
Access type	Accès libre
Publication date	2019
Language	Anglais
Journal information	"Journal of Time Series Analysis" - Vol. 40, p. 3-22 (2019)
Peer reviewed	yes
Publisher	Wiley
issn	0143-9782
Publication status	Publié
Affiliation	UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords	Multivariate time series ; cross-coherence ; dual frequency coherence ; Fourier transform ; harmonizable processes ; evolutionary coherence ; Loève spectrum ; spectral analysis
Links	https://doi.org/10.1111/jtsa.12408[DOI] http://hdl.handle.net/2078.1/203145[Handle]

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See also
	[boreal:146544]	Time-Dependent Dual-Frequency Coherence in Multivariate Non-Stationary Time Series