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The dependencies of the lagged (Pearson) correlation function on thecoefficients of multivariate autoregressive models are interpreted in theframework of time series graphs. Time series graphs are related to the conceptof Granger causality and encode the conditional independence structure of amultivariate process. The authors show that the complex dependencies of thePearson correlation coefficient complicate an interpretation and propose anovel partial correlation measure with a straightforward graph-theoreticalinterpretation. The novel measure has the additional advantage that itssampling distribution is not affected by serial dependencies like that of thePearson correlation coefficient. In an application to climatological timeseries the potential of the novel measure is demonstrated.

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