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Crossing penalised CAViaR

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  • Tibor Szendrei

Abstract

Dynamic quantiles, or Conditional Autoregressive Value at Risk (CAViaR) models, have been extensively studied at the individual level. However, efforts to estimate multiple dynamic quantiles jointly have been limited. Existing approaches either sequentially estimate fitted quantiles or impose restrictive assumptions on the data generating process. This paper fills this gap by proposing an objective function for the joint estimation of all quantiles, introducing a crossing penalty to guide the process. Monte Carlo experiments and an empirical application on the FTSE100 validate the effectiveness of the method, offering a flexible and robust approach to modelling multiple dynamic quantiles in time-series data.

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  • Tibor Szendrei, 2025. "Crossing penalised CAViaR," Papers 2501.10564, arXiv.org.
    • Handle: RePEc:arx:papers:2501.10564
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    References listed on IDEAS

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    1. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
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    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    5. Len Umantsev & Victor Chernozhukov, 2001. "Conditional value-at-risk: Aspects of modeling and estimation," Empirical Economics, Springer, vol. 26(1), pages 271-292.
    6. Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
    7. Chen, Cathy W.S. & Gerlach, Richard & Hwang, Bruce B.K. & McAleer, Michael, 2012. "Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range," International Journal of Forecasting, Elsevier, vol. 28(3), pages 557-574.
    8. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    9. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
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