Convergent Cross-Mapping and Pairwise Asymmetric Inference

TL;DR

This paper critically examines Convergent Cross-Mapping (CCM), revealing its limitations in identifying causality, and introduces Pairwise Asymmetric Inference (PAI) as a modified approach that better aligns with intuitive causal relationships in time series data.

Contribution

The paper demonstrates the limitations of CCM in causality detection and proposes PAI as a novel modification that improves causal inference accuracy.

Findings

CCM correlations do not always match intuitive causality concepts

CCM causality depends on system parameters, not just data

PAI effectively identifies asymmetric causal relationships in examples

Abstract

Convergent Cross-Mapping (CCM) is a technique for computing specific kinds of correlations between sets of times series. It was introduced by Sugihara et al. and is reported to be "a necessary condition for causation" capable of distinguishing causality from standard correlation. We show that the relationships between CCM correlations proposed in \cite{Sugihara2012} do not, in general, agree with intuitive concepts of "driving", and as such, should not be considered indicative of causality. It is shown that CCM causality analysis implies causality is a function of system parameters for simple linear and nonlinear systems. For example, in a RL circuit, both voltage and current can be identified as the driver depending on the frequency of the source voltage. It is shown that CCM causality analysis can, however, be modified to identify asymmetric relationships between pairs of time series that are consistent with intuition for the considered example systems for which CCM causality analysis provided non-intuitive driver identifications. This modification of the CCM causality analysis is introduced as "pairwise asymmetric inference" (PAI) and examples of its use are presented.