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

52 Pages Posted: 24 Jun 2020 Last revised: 29 Mar 2021

See all articles by Andrii Babii

## Andrii Babii

University of North Carolina at Chapel Hill

## Eric Ghysels

University of North Carolina Kenan-Flagler Business School; University of North Carolina (UNC) at Chapel Hill - Department of Economics

## Jonas Striaukas

Louvain Finance; UC Louvain and F.R.S.-FNRS

Date Written: May 29, 2020

### 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 and develop the inferential theory in the high-dimensional setting. To recognize the time series data structures we focus on the sparse-group 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 sparse-group 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 $\tau$-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.

Keywords: HAC Estimator, Sparse-Group LASSO, High-Dimensional Time Series, Inference for Groups, Fuk-Nagaev Inequality, τ-Dependent Sequences

JEL Classification: C52, C55, C58

Suggested Citation

Babii, Andrii and Ghysels, Eric and Striaukas, Jonas and Striaukas, Jonas, High-Dimensional Granger Causality Tests with an Application to VIX and News (May 29, 2020). Available at SSRN: https://ssrn.com/abstract=3615718 or http://dx.doi.org/10.2139/ssrn.3615718