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Conditional quantiles and tail dependence

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  • Bernard, Carole
  • Czado, Claudia

Abstract

Conditional quantile estimation is a crucial step in many statistical problems. For example, the recent work on systemic risk relies on estimating risk conditional on an institution being in distress or conditional on being in a crisis (Adrian and Brunnermeier, 2010; Brownlees and Engle, 2011). Specifically, the CoVaR systemic risk measure is based on a conditional quantile when one of the variable is in the tail of the distribution. In this paper, we study properties of conditional quantiles and how they relate to properties of the copula. In particular, we provide a new graphical characterization of tail dependence and intermediate tail dependence from plots of conditional quantiles with normalized marginal distributions (probit scale). A popular method to estimate conditional quantiles is the quantile regression (Koenker, 2005; Koenker and Bassett, 1978). We discuss the properties and pitfalls of this estimation approach.

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  • Bernard, Carole & Czado, Claudia, 2015. "Conditional quantiles and tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 104-126.
    • Handle: RePEc:eee:jmvana:v:138:y:2015:i:c:p:104-126
    DOI: 10.1016/j.jmva.2015.01.011
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    2. Irresberger, Felix & Weiß, Gregor N.F. & Gabrysch, Janet & Gabrysch, Sandra, 2018. "Liquidity tail risk and credit default swap spreads," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1137-1153.
    3. Holger Fink & Yulia Klimova & Claudia Czado & Jakob Stöber, 2017. "Regime Switching Vine Copula Models for Global Equity and Volatility Indices," Econometrics, MDPI, vol. 5(1), pages 1-38, January.
    4. Nam Gang Lee, 2020. "Vulnerable Growth: A Revisit," Working Papers 2020-22, Economic Research Institute, Bank of Korea.
    5. Chang, Bo & Joe, Harry, 2019. "Prediction based on conditional distributions of vine copulas," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 45-63.
    6. Montes-Rojas, Gabriel, 2017. "Reduced form vector directional quantiles," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 20-30.
    7. Çekin, Semih Emre & Pradhan, Ashis Kumar & Tiwari, Aviral Kumar & Gupta, Rangan, 2020. "Measuring co-dependencies of economic policy uncertainty in Latin American countries using vine copulas," The Quarterly Review of Economics and Finance, Elsevier, vol. 76(C), pages 207-217.
    8. Niemierko, Rochus & Töppel, Jannick & Tränkler, Timm, 2019. "A D-vine copula quantile regression approach for the prediction of residential heating energy consumption based on historical data," Applied Energy, Elsevier, vol. 233, pages 691-708.
    9. Olukunle O. Owolabi & Kathryn Lawson & Sanhita Sengupta & Yingsi Huang & Lan Wang & Chaopeng Shen & Mila Getmansky Sherman & Deborah A. Sunter, 2022. "A Robust Statistical Analysis of the Role of Hydropower on the System Electricity Price and Price Volatility," Papers 2203.02089, arXiv.org.
    10. Hua, Lei & Polansky, Alan & Pramanik, Paramahansa, 2019. "Assessing bivariate tail non-exchangeable dependence," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    11. Christis Katsouris, 2021. "Optimal Portfolio Choice and Stock Centrality for Tail Risk Events," Papers 2112.12031, arXiv.org.
    12. Harry Joe, 2018. "Dependence Properties of Conditional Distributions of some Copula Models," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 975-1001, September.
    13. Sifat, Imtiaz & Ghafoor, Abdul & Ah Mand, Abdollah, 2021. "The COVID-19 pandemic and speculation in energy, precious metals, and agricultural futures," Journal of Behavioral and Experimental Finance, Elsevier, vol. 30(C).
    14. Holger Fink & Yulia Klimova & Claudia Czado & Jakob Stober, 2016. "Regime switching vine copula models for global equity and volatility indices," Papers 1604.05598, arXiv.org.
    15. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    16. Matthias Fischer & Daniel Kraus & Marius Pfeuffer & Claudia Czado, 2017. "Stress Testing German Industry Sectors: Results from a Vine Copula Based Quantile Regression," Risks, MDPI, vol. 5(3), pages 1-13, July.
    17. Tepegjozova Marija & Zhou Jing & Claeskens Gerda & Czado Claudia, 2022. "Nonparametric C- and D-vine-based quantile regression," Dependence Modeling, De Gruyter, vol. 10(1), pages 1-21, January.
    18. Jaworski Piotr, 2017. "On Conditional Value at Risk (CoVaR) for tail-dependent copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 1-19, January.
    19. Navarro Jorge, 2020. "Bivariate box plots based on quantile regression curves," Dependence Modeling, De Gruyter, vol. 8(1), pages 132-156, January.
    20. Bianchi, Michele Leonardo & De Luca, Giovanni & Rivieccio, Giorgia, 2023. "Non-Gaussian models for CoVaR estimation," International Journal of Forecasting, Elsevier, vol. 39(1), pages 391-404.
    21. Navarro Jorge, 2020. "Bivariate box plots based on quantile regression curves," Dependence Modeling, De Gruyter, vol. 8(1), pages 132-156, January.
    22. Michele Leonardo Bianchi & Giovanni De Luca & Giorgia Rivieccio, 2020. "CoVaR with volatility clustering, heavy tails and non-linear dependence," Papers 2009.10764, arXiv.org.
    23. Arief Hakim & Khreshna Syuhada, 2023. "Formulating MCoVaR to Quantify Joint Transmissions of Systemic Risk across Crypto and Non-Crypto Markets: A Multivariate Copula Approach," Risks, MDPI, vol. 11(2), pages 1-45, February.

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