Journal
JOURNAL OF ECONOMETRICS
Volume 238, Issue 2, Pages -Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.jeconom.2023.105554
Keywords
Residual bootstrap; Value-at-Risk; GARCH
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This paper proposes a fixed-design residual bootstrap method for the two-step estimator associated with the conditional Value-at-Risk. The consistency of the bootstrap is proven for a general class of volatility models, and intervals are constructed for the conditional Value-at-Risk. Simulation results show that the reversed-tails bootstrap interval provides accurate coverage compared to the equal-tailed percentile bootstrap interval.
A fixed-design residual bootstrap method is proposed for the two-step estimator of Francq and Zakoian(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 recursivedesign 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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