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A Residual Bootstrap for Conditional Expected Shortfall

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  • Alexander Heinemann
  • Sean Telg

Abstract

This paper studies a fixed-design residual bootstrap method for the two-step estimator of Francq and Zako\"ian (2015) associated with the conditional Expected Shortfall. For a general class of volatility models the bootstrap is shown to be asymptotically valid under the conditions imposed by Beutner et al. (2018). A simulation study is conducted revealing that the average coverage rates are satisfactory for most settings considered. There is no clear evidence to have a preference for any of the three proposed bootstrap intervals. This contrasts results in Beutner et al. (2018) for the VaR, for which the reversed-tails interval has a superior performance.

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  • Alexander Heinemann & Sean Telg, 2018. "A Residual Bootstrap for Conditional Expected Shortfall," Papers 1811.11557, arXiv.org.
    • Handle: RePEc:arx:papers:1811.11557
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    References listed on IDEAS

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    1. Giuseppe Cavaliere & Rasmus Søndergaard Pedersen & Anders Rahbek, 2018. "The Fixed Volatility Bootstrap for a Class of Arch(q) Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 920-941, November.
    2. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    3. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    4. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org, revised Jan 2019.
    5. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2018. "A Residual Bootstrap for Conditional Value-at-Risk," Papers 1808.09125, arXiv.org, revised Aug 2023.
    6. Gao, Feng & Song, Fengming, 2008. "ESTIMATION RISK IN GARCH VaR AND ES ESTIMATES," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1404-1424, October.
    7. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    8. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
    9. Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(1), pages 87-107, Winter.
    10. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    11. Martins-Filho, Carlos & Yao, Feng & Torero, Maximo, 2018. "Nonparametric Estimation Of Conditional Value-At-Risk And Expected Shortfall Based On Extreme Value Theory," Econometric Theory, Cambridge University Press, vol. 34(1), pages 23-67, February.
    12. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2006. "Bootstrap prediction for returns and volatilities in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2293-2312, May.
    13. Osmundsen, Kjartan Kloster, 2018. "Using expected shortfall for credit risk regulation," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 57(C), pages 80-93.
    14. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
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    Cited by:

    1. Alexander Heinemann, 2019. "A Bootstrap Test for the Existence of Moments for GARCH Processes," Papers 1902.01808, arXiv.org, revised Jul 2019.

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