Causal Inference in Time Series in Terms of Rényi Transfer Entropy

Area of Science:

• Nonlinear time series analysis
• Information theory
• Causal inference

Background:

• Uncovering causal interdependencies in observational data is challenging.
• Traditional methods may not capture nonlinear dynamics or extreme events.
• Information-theoretic measures offer alternative approaches.

Purpose of the Study:

• To investigate Rényi's transfer entropy for quantifying causal interdependencies in bivariate time series.
• To explore the role of Rényi's parameter α in controlling information flow.
• To connect Rényi entropy-based methods with traditional autoregressive approaches.

Main Methods:

• Utilized Rényi's information measure and transfer entropy.
• Proved equivalence between Granger causality and Rényi transfer entropy for Gaussian variables.
• Extended results to α-Gaussian variables.
• Employed the Leonenko et al. entropy estimator.
• Analyzed coupled Rössler systems.

Main Results:

• Rényi's transfer entropy effectively quantifies causal interdependencies, especially for "black swan" events.
• Demonstrated equivalence between Granger causality and Rényi transfer entropy for Gaussian and partially for α-Gaussian variables.
• Identified a synchronization threshold and transient regime in coupled Rössler systems.
• Successfully inferred coupling direction for strengths below the transient regime onset.

Conclusions:

• Rényi's transfer entropy is a potent tool for causal inference in nonlinear time series.
• The parameter α allows fine-tuning information transfer analysis.
• This approach bridges information-theoretic and autoregressive methods for data-driven causality.
• Rényi's transfer entropy provides insights into complex dynamics like synchronization and transient regimes.