  Convergent Cross-Mapping (CCM) has shown high potential to perform causal
inference in the absence of models. We assess the strengths and weaknesses of
the method by varying coupling strength and noise levels in coupled logistic
maps. We find that CCM fails to infer accurate coupling strength and even
causality direction in synchronized time-series and in the presence of
intermediate coupling. We find that the presence of noise deterministically
reduces the level of cross-mapping fidelity, while the convergence rate
exhibits higher levels of robustness. Finally, we propose that controlled noise
injections in intermediate-to-strongly coupled systems could enable more
accurate causal inferences. Given the inherent noisy nature of real-world
systems, our findings enable a more accurate evaluation of CCM applicability
and advance suggestions on how to overcome its weaknesses.
