Detecting causality in the frequency domain with Cross-Mapping Coherence

Abstract

Understanding causal relationships within a system is crucial for uncovering its underlying mechanisms. Causal discovery methods, which facilitate the construction of such models from time series data, hold the potential to significantly advance scientific and engineering fields.

This study introduces the Cross-Mapping Coherence (CMC) method, designed to reveal causal connections in the frequency domain between time series. CMC builds upon nonlinear state-space reconstruction and extends the Convergent Cross-Mapping algorithm to the frequency domain by utilizing coherence metrics for evaluation. We tested the CMC method using simulations of logistic maps, Lorenz systems, Kuramoto oscillators, and the Wilson–Cowan model of the visual cortex. CMC accurately identified the direction of causal connections in these simulated scenarios. When applied to the Wilson–Cowan model, CMC was able to disentangle feedforward alpha and feedback gamma coupling between the V1 and V4 areas, supporting the results of previous analysis.

Furthermore, CMC could detect weak connections ($C=0.05$), demonstrated sample efficiency ($L=700$), and maintained robustness in the presence of noise up to $\mathrm{SNR}=10$ on unidirectionally coupled logistic map systems.

In conclusion, the capability to determine directed causal influences across different frequency bands allows CMC to provide valuable insights into the dynamics of complex, nonlinear systems.