On the graph-theoretical interpretation of Pearson correlations in a multivariate process and a novel partial correlation measure

The dependencies of the lagged (Pearson) correlation function on the coecients of multivariate autoregressive models are interpreted in the framework of time series graphs. Time series graphs are related to the concept of Granger causality and encode the conditional independence structure of a multivariate process. The authors show that the complex dependencies of the Pearson correlation coecient complicate an interpretation and propose a novel partial correlation measure with a straightforward graph-theoretical interpretation. The novel measure has the additional advantage that its sampling distribution is not aected by serial dependencies like that of the Pearson correlation coecient. In an application to climatological time series the potential of the novel measure is demonstrated.