We study Granger causality testing for high-dimensional time series using regularized regressions. To perform proper inference, we rely on heteroskedasticity and autocorrelation consistent (HAC) estimation of the asymptotic variance and develop the inferential theory in the high-dimensional setting. To recognize the time-series data structures, we focus on the sparse-group LASSO (sg-LASSO) estimator, which includes the LASSO and the group LASSO as special cases. We establish the debiased central limit theorem for low-dimensional groups of regression coefficients and study the HAC estimator of the long-run variance based on the sg-LASSO residuals. This leads to valid time-series inference for individual regression coefficients as well as groups, including Granger causality tests. The treatment relies on a new Fuk–Nagaev inequality for a class of τ-mixing processes with heavier than Gaussian tails, which is of independent interest. In an empirical application, we study the Granger causal relationship between the VIX and financial news.

中文翻译：

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应用于 VIX 和新闻的高维格兰杰因果检验

我们使用正则化回归研究高维时间序列的格兰杰因果检验。为了进行适当的推理，我们依赖于渐近方差的异方差和自相关一致 (HAC) 估计，并在高维环境中发展推理理论。为了识别时间序列数据结构，我们关注稀疏组 LASSO (sg-LASSO) 估计器，其中包括 LASSO 和组 LASSO 作为特例。我们建立了低维回归系数组的去偏中心极限定理，并研究了基于 sg-LASSO 残差的长期方差的 HAC 估计量。这导致对个体回归系数和组的有效时间序列推断，包括格兰杰因果检验。该处理依赖于新的 Fuk-Nagaev 不等式，用于一类具有比高斯尾重的 τ 混合过程，这是具有独立意义的。在实证应用中，我们研究了波动率指数与财经新闻之间的格兰杰因果关系。