Frequency Domain Repercussions of Instantaneous Granger Causality.

Area of Science:

• Neuroscience
• Information Theory
• Time Series Analysis

Background:

• Directed Transfer Function (DTF) and Partial Directed Coherence (PDC) are established methods for analyzing Granger causality in the frequency domain.
• Existing frameworks may not fully capture instantaneous interactions between time series.

Purpose of the Study:

• To extend the theoretical framework for Granger causality analysis.
• To unify frequency domain methods (DTF, PDC) with instantaneous Granger causality (iGC).
• To provide a comprehensive perspective on directed interactions in time series.

Main Methods:

• Utilized information versions of DTF and PDC.
• Incorporated the frequency domain description of instantaneous Granger causality (iGC).
• Employed standard vector autoregressive (VAR) models.

Main Results:

• Developed a unified theoretical framework for Granger causality analysis.
• Demonstrated that VAR models can represent iGC.
• Showed that instantaneous interactions between time series can be detected using this unified approach.

Conclusions:

• The proposed framework offers a unified perspective on Granger causality in the frequency domain.
• Standard VAR models are capable of portraying instantaneous Granger causality.
• This approach facilitates the detection of non-delayed interactions in time series data.