High-Dimensional Granger Causality Tests with an Application to VIX and News

Abstract 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 develop inferential theory in setting. recognize time-series data structures, focus sparse-group LASSO (sg-LASSO) estimator, which includes group as special cases. establish debiased central limit theorem low-dimensional groups regression coefficients HAC estimator long-run based sg-LASSO residuals. This leads to valid inference individual well groups, including tests. The treatment relies a new Fuk–Nagaev inequality class τ-mixing processes with heavier than Gaussian tails, is independent interest. In an empirical application, causal relationship between VIX financial news.