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. Using this graphical representation, we consider the problem of variable choice. We use the relations among the strongly connected components to select variables that need to be included in a VAR if interest is in impulse response analysis of a given set of variables. Our theoretical contributions 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. An empirical application illustrates 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’.

中文翻译：

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大向量自回归模型中的有向图和变量选择

我们将向量自回归 (VAR) 模型中变量之间的动态关系表示为有向图。基于这些图，我们确定了所谓的强连通分量。使用这个图形表示，我们考虑变量选择的问题。如果对给定变量集的脉冲响应分析感兴趣，我们使用强连通分量之间的关系来选择需要包含在 VAR 中的变量。我们的理论贡献表明，通过将图中的路径与“直接”VAR 表示的系数相关联，从图形方法中选择的变量集与感兴趣变量的多步因果变量集一致。一个实证应用说明了所建议方法的有用性：