Detecting nonlinear causal interactions between dynamical systems by non-uniform embedding of multiple time series

Area of Science:

• Dynamical systems analysis
• Information theory
• Neuroscience

Background:

• Granger causality is a fundamental concept for inferring directed relationships in time series data.
• Traditional Granger causality methods often struggle with nonlinear dynamics and multivariate systems.
• Accurate causality detection is crucial for understanding complex interactions in various scientific domains.

Purpose of the Study:

• To introduce and validate a new approach for detecting nonlinear Granger causality in multivariate time series.
• To quantify causal coupling between dynamical systems using a measure of unpredictability.
• To assess the method's performance on both simulated and real-world data.

Main Methods:

• Embedding multivariate time series using a sequential, non-uniform procedure.
• Utilizing corrected conditional entropy (CCE) as the core measure of unpredictability.
• Quantifying causal coupling as the relative decrease in CCE when incorporating a source system's time series into the target system's embedding.

Main Results:

• The approach successfully detected nonlinear causality in simulated systems with both unidirectional and bidirectional couplings.
• Application to magnetoencephalographic (MEG) data revealed causal coupling patterns consistent with cross-modal sensory processing.
• The method demonstrates robust performance in identifying directed influences in complex data.

Conclusions:

• The developed method offers a powerful tool for nonlinear Granger causality detection in multivariate time series.
• This approach has significant implications for understanding causal interactions in neuroscience and other complex systems.
• The findings support the hypothesis of cross-modal processing in the studied cognitive experiment.