Spectral Dependence

Abstract

This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in 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. This paper also introduces related approaches for modeling dependence through phase-amplitude coupling and causality of (one-sided) filtered signals.

Brain Connectivity Analysis in Distinct Footwear Conditions during Infinity Walk Using fNIRS

“…, Φ L } are M × M coefficient matrices. Despite their linear nature, VAR models can capture the time dynamics [34] and the spectral characteristics of a wide variety of systems [35,36].…”

Break point detection for functional covariance

“…There is also one interesting point in Setting 3 that needs to be emphasized. The two important elements in frequency domain analysis are spectra and phase (see, e.g., Ombao & Pinto, 2021). As testing the structural break in brain signal recordings (e.g., EEG, LPF), we can check the spectrum function (see e.g., Schröder & Ombao, 2019).…”