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BLOCK BOOTSTRAP HAC ROBUST TESTS: THE SOPHISTICATION OF THE NAIVE BOOTSTRAP

Published online by Cambridge University Press:  08 March 2011

Sílvia Gonçalves  and
Timothy J. Vogelsang
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Abstract

This paper studies the properties of naive block bootstrap tests that are scaled by zero frequency spectral density estimators (long-run variance estimators). The naive bootstrap is a bootstrap where the formula used in the bootstrap world to compute standard errors is the same as the formula used on the original data. Simulation evidence shows that the naive bootstrap can be much more accurate than the standard normal approximation. The larger the HAC bandwidth, the greater the improvement. This improvement holds for a large number of popular kernels, including the Bartlett kernel, and it holds when the independent and identically distributed (i.i.d.) bootstrap is used and yet the data are serially correlated. Using recently developed fixed-b asymptotics for HAC robust tests, we provide theoretical results that can explain the finite sample patterns. We show that the block bootstrap, including the special case of the i.i.d. bootstrap, has the same limiting distribution as the fixed-b asymptotic distribution. For the special case of a location model, we provide theoretical results that suggest the naive bootstrap can be more accurate than the standard normal approximation depending on the choice of the bandwidth and the number of finite moments in the data. Our theoretical results lay the foundation for a bootstrap asymptotic theory that is an alternative to the traditional approach based on Edgeworth expansions.

Type
Research Article
Information
Econometric Theory , Volume 27 , Issue 4 , August 2011 , pp. 745 - 791
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

For helpful comments and suggestions we thank an editor and two anonymous referees, Lutz Kilian, Guido Kuersteiner, Nour Meddahi, Ulrich Mueller, Pierre Perron, Yixiao Sun, Hal White, and seminar participants at Boston University, Queen’s University. University of Toronto, University of Western Ontario, Johns Hopkins Biostatistics, Chicago GSB, UCLA, UCSD, University of Michigan, University of Laval, University of Pittsburgh, University of Wisconsin, Cornell University, University of Nottingham, ISEG, Banco de Portugal, the 2007 European Meetings of the Econometric Society in Budapest, the 2005 Winter Meetings of the Econometrics Society in Philadelphia, the 2005 European Economic Association Meetings in Amsterdam and the 2004 Forecasting Conference at Duke University. Vogelsang acknowledges financial support from the NSF through grant SES-0525707, and Gonçalves acknowledges financial support from the SSHRCC.

References

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