On the evaluation of information flow in multivariate systems by the directed transfer function

Area of Science:

• Neuroscience
• Time Series Analysis
• Information Theory

Background:

• The directed transfer function (DTF) is a widely used metric for quantifying information flow in multivariate time series data.
• Accurate interpretation of DTF is crucial for understanding directed relationships and causal influences within complex systems.

Purpose of the Study:

• To clarify the interpretation of the directed transfer function (DTF).
• To compare DTF with other measures of directed relationships.
• To investigate the statistical properties and significance testing of DTF.

Main Methods:

• Comparative analysis of DTF with Granger causality and impulse response functions.
• Spectral analysis of information flow.
• Investigation of statistical properties and development of a significance level for DTF.

Main Results:

• DTF does not directly measure multivariate or bivariate Granger causality.
• DTF is closely related to impulse response functions, serving as a spectral measure of total causal influence.
• A method for establishing a significance level for DTF has been developed.

Conclusions:

• The DTF provides a valuable spectral perspective on causal influence between time series components.
• DTF complements, rather than replaces, traditional causality measures like Granger causality.
• The established significance level allows for robust hypothesis testing regarding information flow.