Testing for Causal Influence using a Partial Coherence Statistic
Abstract
In this paper we explore partial coherence as a tool for evaluating causal influence of one signal sequence on another. In some cases the signal sequence is sampled from a time- or space-series. The key idea is to establish a connection between questions of causality and questions of partial coherence. Once this connection is established, then a scale-invariant partial coherence statistic is used to resolve the question of causality. This coherence statistic is shown to be a likelihood ratio, and its null distribution is shown to be a Wilks Lambda. It may be computed from a composite covariance matrix or from its inverse, the information matrix. Numerical experiments demonstrate the application of partial coherence to the resolution of causality. Importantly, the method is model-free, depending on no generative model for causality.
Cite
@article{arxiv.2112.03987,
title = {Testing for Causal Influence using a Partial Coherence Statistic},
author = {Louis L. Scharf and Yuan Wang},
journal= {arXiv preprint arXiv:2112.03987},
year = {2021}
}