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

Author

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  • Andrii Babii
  • Eric Ghysels
  • Jonas Striaukas

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.

Suggested Citation

  • Andrii Babii & Eric Ghysels & Jonas Striaukas, 2024. "High-Dimensional Granger Causality Tests with an Application to VIX and News," Journal of Financial Econometrics, Oxford University Press, vol. 22(3), pages 605-635.
    • Handle: RePEc:oup:jfinec:v:22:y:2024:i:3:p:605-635.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbac023
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    Cited by:

    1. Andrii Babii & Xi Chen & Eric Ghysels & Rohit Kumar, 2020. "Binary Choice under Asymmetric Loss in a Data-Rich Environment: Theory and an Application to Algorithmic Fairness," Papers 2010.08463, arXiv.org, revised Nov 2025.
    2. Andrii Babii & Ryan T. Ball & Eric Ghysels & Jonas Striaukas, 2024. "Panel data nowcasting: The case of price–earnings ratios," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(2), pages 292-307, March.
    3. Eugene Dettaa & Endong Wang, 2024. "Inference in High-Dimensional Linear Projections: Multi-Horizon Granger Causality and Network Connectedness," Papers 2410.04330, arXiv.org.
    4. Babii, Andrii & Ball, Ryan T. & Ghysels, Eric & Striaukas, Jonas, 2023. "Machine learning panel data regressions with heavy-tailed dependent data: Theory and application," Journal of Econometrics, Elsevier, vol. 237(2).
    5. Andrii Babii, 2022. "High-Dimensional Mixed-Frequency IV Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1470-1483, October.
    6. Brownlees, Christian & Guđmundsson, Guđmundur Stefán, 2025. "Performance Of Empirical Risk Minimization For Linear Regression With Dependent Data," Econometric Theory, Cambridge University Press, vol. 41(2), pages 391-420, April.
    7. Beyhum, Jad & Striaukas, Jonas, 2024. "Testing for sparse idiosyncratic components in factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 244(1).
    8. Yeonwoo Rho & Yun Liu & Hie Joo Ahn, 2020. "Revealing Cluster Structures Based on Mixed Sampling Frequencies," Papers 2004.09770, arXiv.org, revised Feb 2021.
    9. Adamek, Robert & Smeekes, Stephan & Wilms, Ines, 2023. "Lasso inference for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 235(2), pages 1114-1143.
    10. Peter Chinloy & Matthew Imes, 2025. "The endogeneity of profitability and investment," Review of Quantitative Finance and Accounting, Springer, vol. 65(2), pages 691-726, August.
    11. Bin Chen & Yuefeng Han & Qiyang Yu, 2025. "Diffusion Index Forecasting with Tensor Data," Papers 2511.02235, arXiv.org, revised Feb 2026.
    12. Andrii Babii & Eric Ghysels & Jonas Striaukas, 2022. "Machine Learning Time Series Regressions With an Application to Nowcasting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1094-1106, June.

    More about this item

    Keywords

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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