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Residual-Based Garch Bootstrap And Second Order Asymptotic Refinement

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  • Jeong, Minsoo

Abstract

The residual-based bootstrap is considered one of the most reliable methods for bootstrapping generalized autoregressive conditional heteroscedasticity (GARCH) models. However, in terms of theoretical aspects, only the consistency of the bootstrap has been established, while the higher order asymptotic refinement remains unproven. For example, Corradi and Iglesias (2008) demonstrate the asymptotic refinement of the block bootstrap for GARCH models but leave the results of the residual-based bootstrap as a conjecture. To derive the second order asymptotic refinement of the residual-based GARCH bootstrap, we utilize the analysis in Andrews (2001, 2002) and establish the Edgeworth expansions of the t-statistics, as well as the convergence of their moments. As expected, we show that the bootstrap error in the coverage probabilities of the equal-tailed t-statistic and the corresponding test-inversion confidence intervals are at most of the order of O(n−1), where the exact order depends on the moment condition of the process. This convergence rate is faster than that of the block bootstrap, as well as that of the first order asymptotic test.

Suggested Citation

  • Jeong, Minsoo, 2017. "Residual-Based Garch Bootstrap And Second Order Asymptotic Refinement," Econometric Theory, Cambridge University Press, vol. 33(3), pages 779-790, June.
    • Handle: RePEc:cup:etheor:v:33:y:2017:i:03:p:779-790_00
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    Cited by:

    1. Lütkepohl, Helmut & Schlaak, Thore, 2019. "Bootstrapping impulse responses of structural vector autoregressive models identified through GARCH," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 41-61.
    2. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    3. 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.
    4. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.
    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. Wang, Xuqin & Li, Muyi, 2023. "Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    7. M. Dolores Jiménez-Gamero & Sangyeol Lee & Simos G. Meintanis, 2020. "Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 682-703, September.

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