High-dimensional Grander Causality Tests with an Application to VIX and News

Andrii Babii, Eric Ghysels*, Jonas Striaukas

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


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.
Original languageEnglish
JournalJournal of Financial Econometrics
Number of pages31
Publication statusPublished - 4 Jul 2022
Externally publishedYes


  • Fat tails
  • Fuk-Nagaev inequality
  • Granger casuality
  • HAC estimator
  • High-dimensional time series
  • Inference
  • Sparse-group LASSO

Cite this