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

TL;DR

This paper interprets Pearson correlations in multivariate time series through graph theory, relates them to Granger causality, and introduces a new partial correlation measure that simplifies interpretation and is robust to serial dependencies.

Contribution

It provides a graph-theoretical interpretation of Pearson correlations and introduces a novel partial correlation measure with better interpretability and sampling properties.

Findings

The new measure offers a straightforward graph-theoretical interpretation.

It is unaffected by serial dependencies in sampling distribution.

Application to climatological data demonstrates its practical utility.

Abstract

The dependencies of the lagged (Pearson) correlation function on the coefficients 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 coefficient 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 affected by serial dependencies like that of the Pearson correlation coefficient. In an application to climatological time series the potential of the novel measure is demonstrated.