Time-Dependent Dual-Frequency Coherence in Multivariate Non-Stationary Time Series
(2014) , 27 pages
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- Abstract
- Coherence is one common metric for cross-dependence between components in multivariate time series. However, standard coherence does not sufficiently model many biological signals with complex dependence structures such as interactions between low frequency oscillations and high frequency oscillations. The notion of low-high frequency cross-dependence, defined in classical harmonizable processes, assumes time-invariance and thus is still inadequate for modeling 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 lo- cal periodograms. The proposed non-parametric estimation procedure does not suffer from model misspecification. It uses the localized fast Fourier transform (FFT) and hence is able to handle massive data. When applied to electroencephalograms, the proposed method uncovers interesting cross- oscillatory interactions that are neglected by the standard approaches.
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Citations
Gorrostieta, C., Ombao, H., & von Sachs, R. (2014). Time-Dependent Dual-Frequency Coherence in Multivariate Non-Stationary Time Series (ISBA Discussion Paper 2014/30). https://hdl.handle.net/2078.5/197425