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

Andrii Babii, Eric Ghysels and Jonas Striaukas

Journal of Financial Econometrics, 2024, vol. 22, issue 3, 605-635

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 (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.

Keywords: fat tails; Fuk–Nagaev inequality; Granger causality; HAC estimator; high-dimensional time series; inference; sparse-group LASSO (search for similar items in EconPapers)
JEL-codes: C10 C12 C22 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (2)

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Working Paper: High-Dimensional Granger Causality Tests with an Application to VIX and News (2021)
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