A framework for assessing frequency domain causality in physiological time series with instantaneous effects

Area of Science:

• Time series analysis
• Complex systems science
• Signal processing

Background:

• Traditional multivariate autoregressive (MVAR) models struggle with zero-lag interactions in multiple time series.
• Existing causality measures often overlook instantaneous effects, limiting their applicability.
• Quantifying directional relationships in complex systems requires advanced modeling techniques.

Purpose of the Study:

• To develop an extended multivariate autoregressive (eMVAR) framework for quantifying directional relations in multiple time series.
• To introduce novel frequency domain causality measures that account for both lagged and instantaneous effects.
• To demonstrate the utility of the eMVAR framework in analyzing real-world physiological data.

Main Methods:

• Development of an extended multivariate autoregressive (eMVAR) model.
• Derivation of novel frequency domain causality measures from the spectral representation of the eMVAR model.
• Application of two model identification approaches for estimating eMVAR models from time-series data.

Main Results:

• The proposed eMVAR framework successfully quantifies directional relations, including significant zero-lag interactions.
• Novel frequency domain causality measures generalize existing methods (e.g., directed coherence) to include instantaneous effects.
• Theoretical examples and applications on cardiovascular variability and EEG data demonstrate the framework's effectiveness in revealing physiological interaction patterns.

Conclusions:

• The eMVAR framework provides a powerful tool for analyzing directional causality in multiple time series, especially when instantaneous effects are present.
• The novel frequency domain causality measures offer enhanced insights into complex system interactions.
• The approach has significant implications for understanding physiological mechanisms from biological signals.