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A Residual Bootstrap for Conditional Value-at-Risk

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  • Eric Beutner
  • Alexander Heinemann
  • Stephan Smeekes

Abstract

A fixed-design residual bootstrap method is proposed for the two-step estimator of Francq and Zako\"ian (2015) associated with the conditional Value-at-Risk. The bootstrap's consistency is proven for a general class of volatility models and intervals are constructed for the conditional Value-at-Risk. A simulation study reveals that the equal-tailed percentile bootstrap interval tends to fall short of its nominal value. In contrast, the reversed-tails bootstrap interval yields accurate coverage. We also compare the theoretically analyzed fixed-design bootstrap with the recursive-design bootstrap. It turns out that the fixed-design bootstrap performs equally well in terms of average coverage, yet leads on average to shorter intervals in smaller samples. An empirical application illustrates the interval estimation.

Suggested Citation

  • Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2018. "A Residual Bootstrap for Conditional Value-at-Risk," Papers 1808.09125, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:1808.09125
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    References listed on IDEAS

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    5. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org, revised Jan 2019.
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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.
    2. Alexander Heinemann & Sean Telg, 2018. "A Residual Bootstrap for Conditional Expected Shortfall," Papers 1811.11557, arXiv.org.
    3. Francq, Christian & Zakoïan, Jean-Michel, 2020. "Virtual Historical Simulation for estimating the conditional VaR of large portfolios," Journal of Econometrics, Elsevier, vol. 217(2), pages 356-380.
    4. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.
    5. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    6. Heil, Thomas L.A. & Peter, Franziska J. & Prange, Philipp, 2022. "Measuring 25 years of global equity market co-movement using a time-varying spatial model," Journal of International Money and Finance, Elsevier, vol. 128(C).
    7. Royer, Julien, 2021. "Conditional asymmetry in Power ARCH($\infty$) models," MPRA Paper 109118, University Library of Munich, Germany.

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