Directed graphs and variable selection in large vector autoregressive models

We represent the dynamic relation among variables in vector autoregressive (VAR) models as directed graphs. Based on these graphs, we identify so-called strongly connected components (SCCs). Using this graphical representation, we consider the problem of variable selection. We use the relations among the strongly connected components to select variables that need to be included in a VAR if interest is in forecasting or impulse response analysis of a given set of variables. We show that the set of selected variables from the graphical method coincides with the set of variables that is multi-step causal for the variables of interest by relating the paths in the graph to the coefficients of the "direct" VAR representation. Empirical applications illustrate the usefulness of the suggested approach: Including the selected variables into a small US monetary VAR is useful for impulse response analysis as it avoids the well-known "price-puzzle". We also find that including the selected variables into VARs typically improves forecasting accuracy at short horizons.