This paper proposes novel inferential procedures for discovering the network Granger causality in high-dimensional vector autoregressive models. In particular, we mainly offer two multiple testing procedures designed to control the false discovery rate (FDR). The first procedure is based on the limiting normal distribution of the $t$-statistics with the debiased lasso estimator. The second procedure is its bootstrap version. We also provide a robustification of the first procedure against any cross-sectional dependence using asymptotic e-variables. 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：本文提出了在高维向量自回归模型中开展网络格兰杰因果关系发现的创新推断方法。我们主要设计了两种旨在控制错误发现率的多重检验程序。第一种程序基于去偏Lasso估计量所对应的t统计量的渐近正态分布，第二种程序为其自助法改进版本。我们进一步利用渐近e变量方法对第一种程序进行了对抗截面相依性的稳健化处理。研究给出了两种程序在FDR控制与统计功效方面的理论性质保证。有限样本证据表明，两种程序均能在维持较高统计功效的同时有效控制FDR。最后，我们将所提方法应用于英国宏观经济变量及区域房价的大规模网络格兰杰因果关系发现。