Causal decomposition in the mutual causation system.

Area of Science:

• Complex Systems Science
• Time Series Analysis
• Causality Research

Background:

• Traditional time series causality inference relies on prediction, potentially missing simultaneous and reciprocal interactions.
• Real-world phenomena often exhibit complex causal dynamics not fully captured by predictive models.

Purpose of the Study:

• To develop a novel causal-decomposition approach for time series analysis.
• To identify causal interactions based on covariation rather than prediction.
• To demonstrate the method's applicability and consistency with existing approaches.

Main Methods:

• Causal-decomposition approach based on covariation: "cause is that which put, the effect follows; and removed, the effect is removed."
• Empirical Mode Decomposition (EMD) to analyze instantaneous phase dependency.
• Application to both stochastic and deterministic systems, including modelled and actual predator-prey systems.

Main Results:

• Causal interaction is encoded in instantaneous phase dependency at specific time scales.
• Removing causal-related intrinsic components diminishes phase dependency.
• The causal-decomposition method shows consistency with existing methods.

Conclusions:

• The causal-decomposition approach offers a new perspective on time series causality, capturing covariation-based interactions.
• The method is broadly applicable to diverse systems and reveals key causal modes.
• This approach enhances understanding of complex causal relationships in nature.