Fourier-domain transfer entropy spectrum

We propose the Fourier-domain transfer entropy spectrum, a generalization of transfer entropy, as a model-free metric of causality. For arbitrary systems, this approach systematically quantifies the causality among their different system components rather than merely analyzing systems as entireties. The generated spectrum offers a rich-information representation of time-varying latent causal relations, efficiently dealing with nonstationary processes and high-dimensional conditions. We demonstrate its validity in the aspects of parameter dependence, statistical significance tests, and sensibility. An open-source multiplatform implementation of this metric is developed and computationally applied on neuroscience data sets and diffusively coupled logistic oscillators.