Granger causality and path diagrams for multivariate time series

In this paper, we introduce path diagrams for multivariate time series which visualize the dynamic relationships among the variables. In these path diagrams, the vertices represent the components of the time series and are connected by arrows or lines according to the nonvanishing parameters in the autoregressive representation of the time series. We show that these path diagrams provide a framework for the analysis of the dependence structure of the time series. In particular, we give sufficient graphical conditions for Granger-noncausality and Granger-noncausality up to a certain horizon.