Testing for Causal Influence using a Partial Coherence Statistic

TL;DR

This paper introduces a model-free method using a scale-invariant partial coherence statistic, linked to likelihood ratios, to evaluate causal influence between signals, applicable to time- or space-series data.

Contribution

It establishes a novel connection between causality and partial coherence, providing a new, model-free statistical test for causal influence based on likelihood ratios.

Findings

The partial coherence statistic is a likelihood ratio.

Null distribution follows Wilks Lambda.

Method effectively resolves causality in numerical experiments.

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.