Bootstrapping Autoregressive Processes with Possible Unit Roots
An important question in applied work is how to bootstrap autoregressive processes involving highly persistent time series of unknown order of integration. In this paper, we show that in many cases of interest in applied work the standard bootstrap algorithm for unrestricted autoregressions remains valid for processes with exact unit roots; no pre-tests are required, at least asymptotically, and applied researchers may proceed as in the stationary case. Specifically, we prove the first-order asymptotic validity of bootstrapping any linear combination of the slope parameters in autoregressive models with drift. We also establish the bootstrap validity for the marginal distribution of slope parameters and for most linear combinations of slope parameters in higher-order autoregressions without drift. The latter result is in sharp contrast to the well-known bootstrap invalidity result for the random walk without drift. A simulation study examines the finite-sample accuracy of the bootstrap approximation both for integrated and for near-integrated processes. We find that in many, but not all circumstances, the bootstrap distribution closely approximates the exact finite- sample distribution.
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 70 (2002)
Issue (Month): 1 (January)
|Contact details of provider:|| Phone: 1 212 998 3820|
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/
More information through EDIRC
|Order Information:|| Web: https://www.econometricsociety.org/publications/econometrica/access/ordering-back-issues Email: |
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cochrane, John H., 1991. "A critique of the application of unit root tests," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 275-284, April.
- Wolf, Michael & Romano, Joseph P., 1998. "Subsampling confidence intervals for the autoregressive root," DES - Working Papers. Statistics and Econometrics. WS 6268, Universidad Carlos III de Madrid. Departamento de Estadística.
- Jeganathan, P., 1991. "On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 7(03), pages 269-306, September.
- Bruce E. Hansen, 1999.
"The Grid Bootstrap And The Autoregressive Model,"
The Review of Economics and Statistics,
MIT Press, vol. 81(4), pages 594-607, November.
- Faust, Jon, 1996. "Near Observational Equivalence and Theoretical size Problems with Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 12(04), pages 724-731, October.
- Blough, Stephen R, 1992. "The Relationship between Power and Level for Generic Unit Root Tests in Finite Samples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 295-308, July-Sept.
- Diebold, F.X. & Kilian, L. & Nerlove, Marc, 2006.
"Time Series Analysis,"
28556, University of Maryland, Department of Agricultural and Resource Economics.
- Zhang, Hu-Ming, 1992. "A log log law for unstable ARMA models with applications to time series analysis," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 173-204, February.
- Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
- Datta, Somnath, 1995. "Limit theory and bootstrap for explosive and partially explosive autoregression," Stochastic Processes and their Applications, Elsevier, vol. 57(2), pages 285-304, June.
- West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
- Lai, T. L. & Wei, C. Z., 1983. "Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 1-23, March.
- Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
- Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:70:y:2002:i:1:p:377-391. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing)or (Christopher F. Baum)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.