This paper proposes novel inferential procedures for the network Granger causality in high-dimensional vector autoregressive models. In particular, we offer two multiple testing procedures designed to control discovered networks' false discovery rate (FDR). The first procedure is based on the limiting normal distribution of the $t$-statistics constructed by the debiased lasso estimator. The second procedure is based on the bootstrap distributions of the $t$-statistics made by imposing the null hypotheses. Their theoretical properties, including FDR control and power guarantee, are investigated. The finite sample evidence suggests that both procedures can successfully control the FDR while maintaining high power. Finally, the proposed methods are applied to discovering the network Granger causality in a large number of macroeconomic variables and regional house prices in the UK.

翻译：本文提出了针对高维向量自回归模型中网络格兰杰因果关系的新型推断方法。具体而言，我们设计了两种多重检验程序，旨在控制所发现网络的错误发现率（FDR）。第一种程序基于由去偏Lasso估计量构建的$t$统计量的极限正态分布。第二种程序基于通过施加原假设得到的$t$统计量的自举分布。我们研究了这两种程序的理论性质，包括FDR控制和功效保证。有限样本证据表明，两种程序均能成功控制FDR，同时保持较高的检验功效。最后，我们将所提出的方法应用于发现英国大量宏观经济变量与区域房价之间的网络格兰杰因果关系。