Causality in Reversed Time Series: Reversed or Conserved?

Area of Science:

• Causal inference
• Complex systems analysis
• Time series analysis

Background:

• Inferring causal relationships is crucial in science, often relying on temporal order.
• Time reversal in bivariate linear systems typically reverses inferred causality.
• Nonlinear chaotic systems may not exhibit this causal reversal.

Purpose of the Study:

• To investigate conditions for causal reversal under time reversal in linear systems.
• To explore how network structure influences causal direction conservation or reversal.
• To develop predictive indices for coupling reversal and conservation.

Main Methods:

• Theoretical analysis of linear vector autoregressive processes.
• Construction of low-dimensional examples.
• Network simulations of random and realistic coupling patterns (e.g., brain, climate).

Main Results:

• Perfect causal coupling reversal under time reversal occurs only under specific conditions.
• Dominant causal direction can be conserved rather than reversed, even in linear systems.
• Asymmetry and anormality indices predict the degree of coupling reversal and conservation.

Conclusions:

• Temporal order is not a universally sufficient condition for causal inference under time reversal.
• Network properties significantly impact the predictability of causal direction.
• Findings have implications for developing more robust causal inference methods.