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BLOCK BOOTSTRAP HAC ROBUST TESTS: THESOPHISTICATION OF THE NAIVEBOOTSTRAP

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 blockbootstrap tests that are scaled by zero frequencyspectral density estimators (long-run varianceestimators). The naive bootstrap is a bootstrapwhere the formula used in the bootstrap world tocompute standard errors is the same as the formulaused on the original data. Simulation evidence showsthat the naive bootstrap can be much more accuratethan the standard normal approximation. The largerthe HAC bandwidth, the greater the improvement. Thisimprovement holds for a large number of popularkernels, including the Bartlett kernel, and it holdswhen the independent and identically distributed(i.i.d.) bootstrap is used and yet the data areserially correlated. Using recently developedfixed-b asymptotics for HACrobust tests, we provide theoretical results thatcan explain the finite sample patterns. We show thatthe block bootstrap, including the special case ofthe i.i.d. bootstrap, has the same limitingdistribution as the fixed-basymptotic distribution. For the special case of alocation model, we provide theoretical results thatsuggest the naive bootstrap can be more accuratethan the standard normal approximation depending onthe choice of the bandwidth and the number of finitemoments in the data. Our theoretical results lay thefoundation for a bootstrap asymptotic theory that isan alternative to the traditional approach based onEdgeworth expansions.

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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 aneditor and two anonymous referees, Lutz Kilian,Guido Kuersteiner, Nour Meddahi, Ulrich Mueller,Pierre Perron, Yixiao Sun, Hal White, and seminarparticipants at Boston University, Queen’sUniversity. University of Toronto, University ofWestern 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 EconometricSociety in Budapest, the 2005 Winter Meetings ofthe Econometrics Society in Philadelphia, the 2005European Economic Association Meetings inAmsterdam and the 2004 Forecasting Conference atDuke University. Vogelsang acknowledges financialsupport from the NSF through grant SES-0525707,and Gonçalves acknowledges financial support fromthe SSHRCC.

References

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