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Granger Causality Testing in High-Dimensional VARs: A Post-Double-Selection Procedure

Author

Listed:
  • Alain Hecq
  • Luca Margaritella
  • Stephan Smeekes

Abstract

We develop an LM test for Granger causality in high-dimensional (HD) vector autoregressive (VAR) models based on penalized least squares estimations. To obtain a test retaining the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out effects of nuisance variables and establish its uniform asymptotic validity. We conduct an extensive set of Monte-Carlo simulations that show our tests perform well under different data generating processes, even without sparsity. We apply our testing procedure to find networks of volatility spillovers and we find evidence that causal relationships become clearer in HD compared to standard low-dimensional VARs.

Suggested Citation

  • Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Granger Causality Testing in High-Dimensional VARs: A Post-Double-Selection Procedure," Journal of Financial Econometrics, Oxford University Press, vol. 21(3), pages 915-958.
    • Handle: RePEc:oup:jfinec:v:21:y:2023:i:3:p:915-958.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbab023
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    Cited by:

    1. Jonas Krampe & Luca Margaritella, 2021. "Factor Models with Sparse VAR Idiosyncratic Components," Papers 2112.07149, arXiv.org, revised May 2022.
    2. Miao, Ke & Phillips, Peter C.B. & Su, Liangjun, 2023. "High-dimensional VARs with common factors," Journal of Econometrics, Elsevier, vol. 233(1), pages 155-183.
    3. Alain Hecq & Marie Ternes & Ines Wilms, 2021. "Hierarchical Regularizers for Mixed-Frequency Vector Autoregressions," Papers 2102.11780, arXiv.org, revised Mar 2022.
    4. Lenard Lieb & Adam Jassem & Rui Jorge Almeida & Nalan Baştürk & Stephan Smeekes, 2025. "Min(d)ing the President: A Text Analytic Approach to Measuring Tax News," American Economic Journal: Macroeconomics, American Economic Association, vol. 17(2), pages 285-314, April.
    5. repec:pra:mprapa:99376 is not listed on IDEAS
    6. Zhang, Chao & Pu, Xingyue & Cucuringu, Mihai & Dong, Xiaowen, 2025. "Forecasting realized volatility with spillover effects: Perspectives from graph neural networks," International Journal of Forecasting, Elsevier, vol. 41(1), pages 377-397.
    7. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    8. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    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. Eugene Dettaa & Endong Wang, 2024. "Inference in High-Dimensional Linear Projections: Multi-Horizon Granger Causality and Network Connectedness," Papers 2410.04330, arXiv.org.
    11. Fan, Yanqin & Han, Fang & Park, Hyeonseok, 2023. "Estimation and inference in a high-dimensional semiparametric Gaussian copula vector autoregressive model," Journal of Econometrics, Elsevier, vol. 237(1).
    12. Gianluca Cubadda, 2025. "VAR Models with an Index Structure: A Survey with New Results," Econometrics, MDPI, vol. 13(4), pages 1-17, October.
    13. Samuel Tabot Enow, 2025. "Multivariate Granger causality between financial markets: Evidence from US, Europe, Asia and Emerging market," International Journal of Business Ecosystem & Strategy (2687-2293), Bussecon International Academy, vol. 7(2), pages 270-275, April.

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    Keywords

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    JEL classification:

    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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