We develop an LM test for Granger causality in high-dimensional (HD) vector autoregressive (VAR) models based on penalized least squares estimations. To obtain a test retaining the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out effects of nuisance variables and establish its uniform asymptotic validity. We conduct an extensive set of Monte-Carlo simulations that show our tests perform well under different data generating processes, even without sparsity. We apply our testing procedure to find networks of volatility spillovers and we find evidence that causal relationships become clearer in HD compared to standard low-dimensional VARs.

中文翻译：

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高维 VAR 中的格兰杰因果检验：双重选择后程序

我们基于惩罚最小二乘估计在高维 (HD) 向量自回归 (VAR) 模型中开发了格兰杰因果关系的 LM 检验。为了在套索完成变量选择后获得保持适当大小的测试，我们提出了一种后双选择程序来部分消除有害变量的影响并建立其一致的渐近有效性。我们进行了大量的蒙特卡罗模拟，表明我们的测试在不同的数据生成过程下表现良好，即使没有稀疏性。我们应用我们的测试程序来寻找波动溢出网络，并且我们发现证据表明，与标准低维 VAR 相比，HD 中的因果关系变得更加清晰。