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Granger因果关系的新型推断程序。具体来说,我们提供了两种多重检验程序,旨在控制发现网络的虚假发现率(FDR)。第一种程序是基于去偏Lasso估计器构造的$t$-统计量的极限正态分布。第二种程序基于对施加了零假设的$t$-统计量的自举分布构造。我们研究了它们的理论性质,包括FDR控制和功率保证。有限样本证据表明,两种程序都可以成功控制FDR,同时保持高功率。最后,我们将所提出的方法应用于发现英国大量的宏观经济变量和区域房价的网络Granger因果关系。