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

TL;DR

This paper develops a new high-dimensional Granger causality testing framework using regularized regressions, HAC variance estimation, and the sparse-group LASSO, enabling valid inference in complex time series data, demonstrated through VIX and news analysis.

Contribution

It introduces a novel inferential approach for high-dimensional Granger causality using sparse-group LASSO and HAC estimation, with theoretical guarantees and an empirical VIX-news case study.

Findings

Valid Granger causality tests for high-dimensional data

Theoretical proof of the debiased CLT for sparse-group LASSO

Empirical evidence of causality between VIX and financial 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 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.