Spectral Dependence

Hernando Ombao and Marco Pinto

Econometrics and Statistics, 2024, vol. 32, issue C, 122-159

Abstract: 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.

Keywords: Causality; Cramér representation; Cross-coherence; Dual-frequency coherence; Fourier transform; Harmonizable processes; Multivariate time series; Spectral Analysis (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecosta:v:32:y:2024:i:c:p:122-159

DOI: 10.1016/j.ecosta.2022.10.005

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