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.
|Date of creation:||01 Aug 2000|
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- Hansen,B.E., 1998.
"The grid bootstrap and the autoregressive model,"
26, Wisconsin Madison - Social Systems.
- 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.
- 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 1057-72, June.
- Francis X. Diebold & Lutz Kilian & Marc Nerlove, 2006.
"Time Series Analysis,"
PIER Working Paper Archive
06-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
- Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
- 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.
- 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.
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