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RESIDUAL-BASED GARCH BOOTSTRAP AND SECOND ORDER ASYMPTOTIC REFINEMENT

Published online by Cambridge University Press:  24 May 2016

Minsoo Jeong
Minsoo Jeong*
Affiliation:
Yonsei UniversityWonju Campus
*
*Address correspondence to Minsoo Jeong, Department of Economics, Yonsei University Wonju Campus, Wonju, Gangwon, 26493, Korea, e-mail: [email protected]
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Abstract

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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.

Type
MISCELLANEA
Information
Econometric Theory , Volume 33 , Issue 3 , June 2017 , pp. 779 - 790
Copyright
Copyright © Cambridge University Press 2016 

Footnotes

The author is very grateful to Joon Y. Park for comments and advice. This paper is based on the author’s master’s thesis written under his guidance. The author also thanks to Joel L. Horowitz for advise during his visit to SNU, and to anonymous reviewers for valuable comments which improved the quality of the paper.

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