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