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Single-Index-Based CoVaR With Very High-Dimensional Covariates


  • Yan Fan
  • Wolfgang Karl Härdle
  • Weining Wang
  • Lixing Zhu


Systemic risk analysis reveals the interdependencies of risk factors especially in tail event situations. In applications the focus of interest is on capturing joint tail behavior rather than a variation around the mean. Quantile and expectile regression are used here as tools of data analysis. When it comes to characterizing tail event curves one faces a dimensionality problem, which is important for CoVaR (Conditional Value at Risk) determination. A projection-based single-index model specification may come to the rescue but for ultrahigh-dimensional regressors one faces yet another dimensionality problem and needs to balance precision versus dimension. Such a balance is achieved by combining semiparametric ideas with variable selection techniques. In particular, we propose a projection-based single-index model specification for very high-dimensional regressors. This model is used for practical CoVaR estimates with a systemically chosen indicator. In simulations we demonstrate the practical side of the semiparametric CoVaR method. The application to the U.S. financial sector shows good backtesting results and indicate market coagulation before the crisis period. Supplementary materials for this article are available online.

Suggested Citation

  • Yan Fan & Wolfgang Karl Härdle & Weining Wang & Lixing Zhu, 2018. "Single-Index-Based CoVaR With Very High-Dimensional Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 212-226, April.
  • Handle: RePEc:taf:jnlbes:v:36:y:2018:i:2:p:212-226
    DOI: 10.1080/07350015.2016.1180990

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    Cited by:

    1. Jun Jin & Tiefeng Ma & Jiajia Dai & Shuangzhe Liu, 2021. "Penalized weighted composite quantile regression for partially linear varying coefficient models with missing covariates," Computational Statistics, Springer, vol. 36(1), pages 541-575, March.
    2. Anna Denkowska & Stanisław Wanat, 2020. "A Tail Dependence-Based MST and Their Topological Indicators in Modeling Systemic Risk in the European Insurance Sector," Risks, MDPI, vol. 8(2), pages 1-22, April.
    3. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.
    4. Xu, Qifa & Li, Mengting & Jiang, Cuixia & He, Yaoyao, 2019. "Interconnectedness and systemic risk network of Chinese financial institutions: A LASSO-CoVaR approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    5. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
    6. Wang, Kangning & Li, Shaomin & Zhang, Benle, 2021. "Robust communication-efficient distributed composite quantile regression and variable selection for massive data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    7. Bonaccolto, Giovanni & Borri, Nicola & Consiglio, Andrea, 2023. "Breakup and default risks in the great lockdown," Journal of Banking & Finance, Elsevier, vol. 147(C).
    8. Xu, Qiuhua & Zhang, Yixuan & Zhang, Ziyang, 2021. "Tail-risk spillovers in cryptocurrency markets," Finance Research Letters, Elsevier, vol. 38(C).
    9. Rong Jiang & Mengxian Sun, 2022. "Single-index composite quantile regression for ultra-high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 443-460, June.
    10. Kangning Wang & Wen Shan, 2021. "Copula and composite quantile regression-based estimating equations for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 441-455, June.
    11. Eliana Christou & Michael Grabchak, 2022. "Estimation of Expected Shortfall Using Quantile Regression: A Comparison Study," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 725-753, August.
    12. Zhang, Xingmin & Zhang, Shuai, 2021. "Optimal time-varying tail risk network with a rolling window approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).

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