  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.
