Causal Decomposition in the Mutual Causation System

TL;DR

This paper introduces a novel causal decomposition method based on instantaneous phase dependency, enabling the analysis of reciprocal causality in complex time series without relying on prediction-based approaches.

Contribution

The paper presents a new causality inference technique using phase dependency, applicable to both stochastic and deterministic systems, addressing limitations of existing prediction-based methods.

Findings

Causal interactions are encoded in phase dependency at specific time scales.

Removing causal components reduces phase dependency, confirming causality.

Method uncovers key causal modes in predator-prey systems.

Abstract

Inference of causality in time series has been principally based on the prediction paradigm. Nonetheless, the predictive causality approach may overlook the simultaneous and reciprocal nature of causal interactions observed in real world phenomena. Here, we present a causal decomposition approach that is not based on prediction, but based on the instantaneous phase dependency between the intrinsic components of a decomposed time series. The method involves two assumptions: (1) any cause effect relationship can be quantified with instantaneous phase dependency between the source and target decomposed as intrinsic components at specific time scale, and (2) the phase dynamics in the target originating from the source are separable from the target itself. Using empirical mode decomposition, we show that the causal interaction is encoded in instantaneous phase dependency at a specific time scale, and this phase dependency is diminished when the causal-related intrinsic component is removed from the effect. Furthermore, we demonstrate the generic applicability of our method to both stochastic and deterministic systems, and show the consistency of the causal decomposition method compared to existing methods, and finally uncover the key mode of causal interactions in both the modelled and actual predator prey system. We anticipate that this novel approach will assist with revealing causal interactions in complex networks not accounted for by current methods.