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Time‐Dependent Dual‐Frequency Coherence in Multivariate Non‐Stationary Time Series
Author(s) -
Gorrostieta Cristina,
Ombao Hernando,
Von Sachs Rainer
Publication year - 2019
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12408
Subject(s) - coherence (philosophical gambling strategy) , estimator , mathematics , time–frequency analysis , component (thermodynamics) , nonparametric statistics , series (stratigraphy) , cross spectrum , algorithm , multivariate statistics , metric (unit) , instantaneous phase , fourier transform , computer science , statistical physics , statistics , frequency domain , mathematical analysis , telecommunications , paleontology , radar , physics , operations management , biology , economics , thermodynamics
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.