A new NARX-based Granger linear and nonlinear casual influence detection method with applications to EEG data

Area of Science:

• Neuroscience
• Signal Processing
• Computational Biology

Background:

• Traditional Granger causality methods often assume linear relationships.
• Analyzing nonlinear dynamics in biological signals like EEG is crucial for understanding complex brain activity.
• Existing methods may struggle to capture the full spectrum of interactions within multivariate and time-varying systems.

Purpose of the Study:

• To introduce a new NARX-based Granger causality method for detecting linear and nonlinear causal influences.
• To develop metrics for assessing signal linearity, nonlinearity, and inter-signal influence.
• To extend the method for analyzing time-varying and multivariate data, with a focus on human EEG.

Main Methods:

• Utilizing Nonlinear Autoregressive Exogenous (NARX) models within a Granger causality framework.
• Developing four specific indices to quantify linearity, nonlinearity, and causal influence between two signals.
• Implementing an Orthogonal Least Squares (OLS) adaptation for efficient model term selection.
• Extending the methodology to handle time-varying and multivariate signal analysis.

Main Results:

• The proposed NARX-based Granger causality method effectively detects both linear and nonlinear causal relationships.
• The developed indices provide robust measures of signal characteristics and interdependencies.
• The algorithm demonstrates successful application to simulated data and real-world human EEG recordings from four patients.

Conclusions:

• The new method offers a powerful tool for dissecting complex linear and nonlinear causal interactions in various data types.
• Its application to EEG data provides a more comprehensive understanding of brain signal dynamics.
• This approach advances the analysis of causality in neuroscience and other fields dealing with complex time-series data.