Hostname: page-component-cb9f654ff-9knnw Total loading time: 0 Render date: 2025-08-16T23:32:38.409Z Has data issue: false hasContentIssue false
  • English
  • Français

BLOCK BOOTSTRAP HAC ROBUST TESTS: THESOPHISTICATION OF THE NAIVEBOOTSTRAP

Published online by Cambridge University Press:  08 March 2011

Sílvia Gonçalves  and
Timothy J. Vogelsang
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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

REFERENCES

Akonom, J. (1993) Comportement asymptotique du temps d’occupation du processus des sommes partielles. Annales de l’Institut Henri Poincare 29, 57–81.Google Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–854.CrossRefGoogle Scholar
Andrews, D.W.K. (2002) Higher-order improvements of a computationally attactive k-step bootstrap for extremum estimators. Econometrica 70, 119–162.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley.Google Scholar
Chang, Y. & Park, J. (2003) A sieve bootstrap for the test of a unit root. Journal of Time Series Analysis 24, 379–400.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.CrossRefGoogle Scholar
Davison, A.C. & Hall, P. (1993) On studentizing and blocking methods for implementing the bootstrap with dependent data. Australian Journal of Statistics 35, 215–224.10.1111/j.1467-842X.1993.tb01327.xCrossRefGoogle Scholar
de Jong, R.M. & Davidson, J. (2000) Consistency of kernel estimators of heteroskedastic and autocorrelated covariance matrices. Econometrica 68, 407–424.CrossRefGoogle Scholar
Fitzenberger, B. (1997) The moving blocks bootstrap and robust inference for linear least squares and quantile regressions. Journal of Econometrics 82, 235–287.CrossRefGoogle Scholar
Götze, F. & Künsch, H.R. (1996) Second-order correctness of the blockwise bootstrap for stationary observations. Annals of Statistics 24, 1914–1933.10.1214/aos/1069362303CrossRefGoogle Scholar
Hall, P. & Horowitz, J.L. (1996) Bootstrap critical values for tests based on generalized method of moments estimators. Econometrica 64, 891–916.CrossRefGoogle Scholar
Hansen, B.E. (1991) Strong laws for dependent heterogeneous processes. Econometric Theory 7, 213–221.CrossRefGoogle Scholar
Hansen, B.E. (1992) Erratum. Econometric Theory 8, 421–422.Google Scholar
Inoue, A. & Shintani, M. (2006) Bootstrapping GMM estimators for time series. Journal of Econometrics 127(2), 531–555.CrossRefGoogle Scholar
Jansson, M. (2004) The error rejection probability of simple autocorrelation robust tests. Econometrica 72, 937–946.CrossRefGoogle Scholar
Kiefer, N.M. & Vogelsang, T.J. (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21, 1130–1164.CrossRefGoogle Scholar
Kunsch, H.R. (1989) The jackknife and the bootstrap for general stationary observations. Annals of Statistics 17, 1217–1241.CrossRefGoogle Scholar
Lahiri, S.N. (1996) On edgeworth expansion and moving block bootstrap for studentized m-estimators in multiple linear regression models. Journal of Multivariate Analysis 56, 42–59.CrossRefGoogle Scholar
Liu, R. & Singh, K. (1992) Moving blocks jackknife and bootstrap capture weak dependence. In LePage, R. & Billiard, L. (eds.), Exploring the Limits of the Bootstrap. Wiley.Google Scholar
Paparoditis, E. & Politis, P. (2003) Residual-based block bootstrap for unit root testing. Econometrica 71, 813–855.10.1111/1468-0262.00427CrossRefGoogle Scholar
Park, J.Y. (2003) Bootstrap unit root tests. Econometrica 71, 1845–1898.CrossRefGoogle Scholar
Park, J.Y. (2006) A bootstrap theory for weakly integrated processes. Journal of Econometrics 133, 639–672.10.1016/j.jeconom.2005.06.009CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Sakhanenko, A.I. (1980) On unimprovable estimates of the rate of convergence in invariance principle. In Colloquia Mathematica Societatis Janos Bolyai 32, Nonparametric Statistical Inference. pp. 779–783. North-Holland.Google Scholar
Singh, K. (1981) On the asymptotic accuracy of Efron’s bootstrap. Annals of Statistics 9, 1187–1195.10.1214/aos/1176345636CrossRefGoogle Scholar
Sun, Y. & Phillips, P. (2009) Optimal Bandwidth Choice for Interval Estimation in GMM Regression. Working Paper, UCSD.Google Scholar
Sun, Y., Phillips, P.C.B., & Jin, S., (2008) Optimal bandwidth selection in heteroskedasticity-autocorrelation robust testing. Econometrica 76, 175–194.CrossRefGoogle Scholar
Velasco, C. & Robinson, P.M. (2001) Edgeworth expansions for spectral density estimates and studentized sample mean. Econometric Theory 17, 497–539.CrossRefGoogle Scholar