Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2025-01-03T08:15:10.599Z Has data issue: false hasContentIssue false
  • English
  • Français

A NOTE ON THE POWER OF BOOTSTRAP UNIT ROOT TESTS

Published online by Cambridge University Press:  08 January 2003

Anders Rygh Swensen
Anders Rygh Swensen
Affiliation:
University of Oslo
Get access Rights & Permissions [Opens in a new window]

Abstract

In this note we consider the asymptotic power functions of some bootstrap unit root tests under local alternatives and show that they are in fact the same as for ordinary unit root tests. This is regardless of whether the differences of the observations, i.e., the so-called restricted residuals, or the ordinary least squares residuals are used to construct the resampled observations. We also consider models containing a constant and a linear trend and the DF-GLS tests proposed by Elliott, Rothenberg, and Stock (1996, Econometrica 64, 813–836). A small Monte Carlo experiment is included.I thank the associate editor, Bruce E. Hansen, and three anonymous referees for very constructive comments on the previous versions of the manuscript.

Type
Research Article
Information
Econometric Theory , Volume 19 , Issue 1 , February 2003 , pp. 32 - 48
Copyright
© 2003 Cambridge University Press

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.)

References

REFERENCES

Banerjee, A., J. Dolado, J.W. Galbraith, & D.F. Hendry (1993) Co-integration, Error-Correction, and the Econometric Analysis of Non-stationary Data. Oxford: Oxford University Press.
Basawa, I.V., A.K. Mallik, W.P. McCormic, J.H. Reeves, & R.L. Taylor (1991a) Bootstrapping unstable first-order autoregressive processes. Annals of Statistics 19, 1098–1101.Google Scholar
Basawa, I.V., A.K. Mallik, W.P. McCormic, J.H. Reeves, & R.L. Taylor (1991b) Bootstrap test of significance and sequential bootstrap estimation for unstable first order autoregressive processes. Communications in Statistics A 20, 1015–1026.Google Scholar
Berkowitz, J. & L. Kilian (2000) Recent developments in bootstrapping time series. Econometric Reviews 19, 1–48.Google Scholar
Chan, N.H. & C.Z. Wei (1987) Asymptotic inference for nearly nonstationary AR(1) processes. Annals of Statistics 15, 1050–1063.Google Scholar
Davidson, R. & J.G. MacKinnon (2000) Bootstrap tests: How many bootstraps? Econometric Reviews 19, 55–68.Google Scholar
Dickey, D.A. & W.A. Fuller (1979) Distributions of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431.Google Scholar
Elliott, G., T.J. Rothenberg, & J.H. Stock (1996) Efficient tests for an autoregressive unit root. Econometrica 64, 813–836.Google Scholar
Ferretti, N. & J. Romo (1996) Unit root bootstrap tests for AR(1) models. Biometrika 83, 849–860.Google Scholar
Fuller, W.A. (1996) Introduction to Statistical Time Series, 2nd ed. New York: Wiley.
Hansen, B.E. (1999) The grid bootstrap and the autoregressive model. Review of Economics and Statistics 81, 594–607.Google Scholar
Heimann, G. & J.-P. Kreiss (1996) Bootstrapping general first order autoregression. Statistics and Probability Letters 30, 87–98.Google Scholar
Li, H. & G.S. Maddala (1996) Bootstrapping time series models. Econometric Reviews 15, 115–158.Google Scholar
Li, H. & G.S. Maddala (1997) Bootstrapping cointegrating regressions. Journal of Econometrics 80, 297–318.Google Scholar
Paparoditis, E. & D.N. Politis (2000) Unit Root Testing via the Continuous-Path Block Bootstrap. Manuscript, University of California, San Diego.
Paparoditis, E. & D.N. Politis (2001) The continuous-path block-bootstrap. In M. Puri (ed.), Asymptotics in Statistics and Probability: Papers in honor of George Roussas, pp. 305–320. Zeist, the Netherlands: VSP Publications.
Phillips, P.C.B. (1987) Towards a unified asymptotic theory for autoregression. Biometrika 74, 535–547.Google Scholar
Phillips, P.C.B. & P. Perron (1988) Testing for a unit root in time series regression. Biometrika 75, 335–346.CrossRefGoogle Scholar
Politis, D.N. & J.P. Romano (1994) The stationary bootstrap. Journal of the American Statistical Association 89, 1303–1313.CrossRefGoogle Scholar
Pollard, D. (1984) Convergence of Stochastic Processes. New York: Springer-Verlag.
Press, W.H., S.A. Teukolsky, W.T. Vetterling, & B.P. Flannery, (1992) Numerical Recipes in Fortran, 2nd ed. Cambridge: Cambridge University Press.
Swensen, A.R. (2002) Bootstrapping unit root tests for integrated processes. Journal of Time Series Analysis, in press.Google Scholar