Quantification of causal couplings via dynamical effects: a unifying perspective

Area of Science:

• Complex Systems Science
• Time Series Analysis
• Causal Inference

Background:

• Quantitative characterization of causal couplings is vital for understanding complex systems.
• Existing statistical tools often aim for universal, model-free quantifiers of coupling strength.
• A clear, universally applicable interpretation for such quantifiers remains elusive.

Purpose of the Study:

• To propose a general conceptual framework for causal coupling quantification.
• To extend concepts of virtual interventions and dynamical causal effects.
• To provide a unifying view of existing measures and introduce new ones with clear interpretations.

Main Methods:

• Utilizing state space models as the foundation for the framework.
• Introducing two basic intervention types: state space and parametric.
• Defining four families of coupling characteristics based on intervention and effect types (orbital/transient, stationary/limit).

Main Results:

• The framework unifies diverse, previously established causal coupling measures.
• New coupling characteristics with definite 'intervention-effect' interpretations are introduced.
• Demonstrates that diverse characteristics cannot be reduced to a single coupling strength quantifier.

Conclusions:

• The interpretation of causal coupling measures is inevitably model-based.
• A single universal quantifier for coupling strength is not feasible.
• The proposed dynamical causal effect measures quantify specific manifestations of coupling within system dynamics.