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Bootstrapping cointegrating regressions

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  • Chang, Yoosoon
  • Park, Joon Y.
  • Song, Kevin

Abstract

In this paper, we consider bootstrapping cointegrating regressions. It is shown that the method of bootstrap, if properly implemented, generally yields consistent estimators and test statistics for cointegrating regressions. We do not assume any specific data generating process, and employ the sieve bootstrap based on the approximated finite-order vector autoregressions for the regression errors and the firrst differences of the regressors. In particular, we establish the bootstrap consistency for OLS method. The bootstrap method can thus be used to correct for the finite sample bias of the OLS estimator and to approximate the asymptotic critical values of the OLS-based test statistics in general cointegrating regressions. The bootstrap OLS procedure, however, is not efficient. For the efficient estimation and hypothesis testing, we consider the procedure proposed by Saikkonen (1991) and Stock and Watson (1993) relying on the regression augmented with the leads and lags of differenced regressors. The bootstrap versions of their procedures are shown to be consistent, and can be used to do inferences that are asymptotically valid. A Monte Carlo study is conducted to investigate the finite sample performances of the proposed bootstrap methods.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 133 (2006)
Issue (Month): 2 (August)
Pages: 703-739

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Handle: RePEc:eee:econom:v:133:y:2006:i:2:p:703-739

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  1. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, 05.
  2. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228 Elsevier.
  3. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
  4. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
  5. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
  6. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  7. Park, Joon, 2002. "Bootstrap Unit Root Tests," Working Papers 2003-04, Rice University, Department of Economics.
  8. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  9. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(02), pages 469-490, April.
  10. Yoosoon Chang, 2000. "Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency," Econometric Society World Congress 2000 Contributed Papers 1585, Econometric Society.
  11. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
  12. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(01), pages 95-131, April.
  13. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, 07.
  14. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
  15. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
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