Comparison of nonlinear Granger causality extensions for low-dimensional systems.

Area of Science:

• Complex Systems Analysis
• Time Series Analysis
• Causality Inference

Background:

• Identifying hidden interdependences in complex systems is crucial for understanding internal dynamics and subsystem interactions.
• System interactions are often nonlinear and asymmetric, posing challenges for traditional analysis methods.
• Noise and limited signal length further constrain the estimation of hidden relationships.

Purpose of the Study:

• To evaluate a nonlinear extension of Granger causality using polynomial embedding for detecting causal dependences.
• To compare the performance of this novel method against three recently proposed alternatives.
• To assess the methods' effectiveness in low-dimensional, low-order-nonlinearity systems with varying noise levels.

Main Methods:

• Focus on causal dependences between bivariate time series.
• Utilized a nonlinear extension of Granger causality incorporating polynomial terms in the embedding vector.
• Compared performance against three alternative causality detection methods.
• Tested methods on artificial chaotic maps with different noise contamination levels.

Main Results:

• The polynomial embedding technique demonstrated success in detecting asymmetric (causal) dependences.
• Effective detection was observed in many low-dimensional bivariate time series scenarios.
• Performance was evaluated across various noise contamination setups.

Conclusions:

• The polynomial embedding extension of Granger causality is a promising tool for uncovering hidden causal relationships in complex systems.
• The method shows robustness in identifying asymmetric interactions within bivariate time series.
• Further research can explore its application in more complex and higher-dimensional systems.