Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous...

Area of Science:

• Time series analysis
• Granger causality
• Network inference

Background:

• Partial Directed Coherence (PDC) and generalized PDC (gPDC) analyze Granger causality in multivariate time series frequency domains.
• These methods are based on multivariate autoregressive (MVAR) models, focusing solely on lagged effects and omitting instantaneous interactions.
• Instantaneous effects are prevalent in experimental data and can impact causality assessments.

Purpose of the Study:

• To investigate the impact of excluding instantaneous effects on PDC and gPDC evaluations.
• To propose and validate an extended MVAR model incorporating both instantaneous and lagged effects.
• To introduce new causality measures: instantaneous PDC (iPDC) and extended PDC (ePDC).

Main Methods:

• Developing an extended MVAR model that includes both lagged and instantaneous effects.
• Evaluating the proposed iPDC and ePDC measures on theoretical MVAR processes.
• Applying iPDC and ePDC to cardiorespiratory and electroencephalogram (EEG) time series data.

Main Results:

• Theoretical examples demonstrate that neglecting instantaneous effects can lead to misleading PDC and gPDC results.
• The proposed ePDC and iPDC accurately interpret extended and lagged causality, respectively.
• Application to cardiorespiratory and EEG data shows ePDC and iPDC offer improved interpretability compared to PDC and gPDC.

Conclusions:

• Excluding instantaneous effects from MVAR models can distort Granger causality analysis.
• The extended MVAR model and its derived measures (iPDC, ePDC) provide a more comprehensive assessment of causality in time series.
• iPDC and ePDC enhance the physiological interpretability of causality in complex systems like cardiorespiratory and neural networks.