Quantifying coupling and causality in dynamic bivariate systems: a unified framework for time-domain, spectral, and...

Area of Science:

• Complex Systems Analysis
• Time Series Analysis
• Network Physiology

Background:

• Understanding complex systems requires quantifying interactions between units.
• Existing methods for assessing interdependence have limitations.

Purpose of the Study:

• To provide a comprehensive description of time, frequency, and information-theoretic measures for assessing interdependence.
• To introduce a unified framework connecting causal, spectral, and information-theoretic metrics.
• To support flexible and robust analyses of statistical dependencies and directional relationships.

Main Methods:

• Introduced classical time and frequency domain correlation-based measures.
• Discussed directional approaches derived from Granger causality.
• Detailed information-theoretic measures of symmetrical and directional coupling.
• Described linear model-based and non-linear model-free estimation approaches (binning, permutation, nearest-neighbour).
• Presented a unified framework for frequency-specific information-theoretic metrics.

Main Results:

• Established a connection between causal and symmetric, spectral and information-theoretic measures.
• Enabled frequency-specific representation of information-theoretic metrics for analyzing oscillatory components.
• Demonstrated practical computation with a software toolbox.
• Applied methods to cardiovascular and climate data.

Conclusions:

• The work bridges theoretical concepts with practical tools for analyzing dynamical behaviors.
• Enables researchers to investigate a wide range of interactions in complex systems.
• Facilitates robust analyses of statistical dependencies and directional relationships in bivariate systems.