Spectral Dependence

A general framework for modeling dependence in multivariate time series is presented. Its fundamental approach relies on decomposing each signal inside a system into various frequency components and then studying the dependence properties through these oscillatory activities. The unifying theme acro...

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Bibliographic Details
Published in:Econometrics and statistics 2024-10, Vol.32, p.122-159
Main Authors: Ombao, Hernando, Pinto, Marco
Format: Article
Language:English
Subjects:
Causality
Cramér representation
Cross-coherence
Dual-frequency coherence
Fourier transform
Harmonizable processes
Multivariate time series
Spectral Analysis
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Summary:A general framework for modeling dependence in multivariate time series is presented. Its fundamental approach relies on decomposing each signal inside a system into various frequency components and then studying the dependence properties through these oscillatory activities. The unifying theme across the paper is to explore the strength of dependence and possible lead-lag dynamics through filtering. The proposed framework is capable of representing both linear and non-linear dependencies that could occur instantaneously or after some delay (lagged dependence). Examples for studying dependence between oscillations are illustrated through multichannel electroencephalograms. These examples emphasized that some of the most prominent frequency domain measures such as coherence, partial coherence, and dual-frequency coherence can be derived as special cases under this general framework. Related approaches for modeling dependence through phase-amplitude coupling and causality of (one-sided) filtered signals are also introduced.
ISSN:2452-3062
2452-3062
DOI:10.1016/j.ecosta.2022.10.005