Explorations of Temporal Causality Using Partial Coherence

In this paper we explore partial coherence as a tool for evaluating the causal, anti-causal or mixed-causal dependence of one time series on another. The key idea is to establish a connection between partial coherence and questions of causality. Once this connection is established, then a scale-invariant partial coherence statistic is used to resolve the question of temporal causality. This coherence statistic is shown to be a likelihood ratio. 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 temporal causality.