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Tests for Cointegration with Structural Breaks Based on Subsamples

  • James Davidson

    (Department of Economics, University of Exeter)

  • Andrea Monticini

    (Department of Economics, University of Exeter)

This paper considers tests for cointegration with allowance for structural breaks, using the extrema of residual-based tests over subsamples of the data. One motivation for the approach is to formalize the practice of data snooping by practitioners, who may examine subsamples after failing to find a predicted cointegrating relationship. Valid critical values for such multiple testing situations may be useful. The methods also have the advantage of not imposing a form for the alternative hypothesis, in particular slope vs. intercept shifts and single versus multiple breaks, and being comparatively easy to compute. A range of alternative subsampling procedures, including sample splits, incremental and rolling samples are tabulated and compared experimentally. Shiller's annual stock prices and dividends series provide an illustration.

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Paper provided by Exeter University, Department of Economics in its series Discussion Papers with number 0704.

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Date of creation: 2007
Date of revision:
Handle: RePEc:exe:wpaper:0704
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  1. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-88, October.
  2. Davidson, James, 1998. "Structural relations, cointegration and identification: some simple results and their application," Journal of Econometrics, Elsevier, vol. 87(1), pages 87-113, August.
  3. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  4. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-93, January.
  5. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, vol. 70(1), pages 99-126, January.
  6. Ignacio N Lobato & Carlos Velasco, 2007. "Efficient Wald Tests for Fractional Unit Roots," Econometrica, Econometric Society, vol. 75(2), pages 575-589, 03.
  7. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(05), pages 621-642, October.
  8. Anindya Banerjee & Robin L. Lumsdaine & James H. Stock, 1990. "Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence," NBER Working Papers 3510, National Bureau of Economic Research, Inc.
  9. Ignacio N. Lobato & Carlos Velasco, 2006. "Optimal Fractional Dickey-Fuller tests," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 492-510, November.
  10. Davidson, James, 2006. "Alternative bootstrap procedures for testing cointegration in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 741-777, August.
  11. Kim, Jae-Young, 2003. "Inference On Segmented Cointegration," Econometric Theory, Cambridge University Press, vol. 19(04), pages 620-639, August.
  12. Davidson, James, 2002. "A model of fractional cointegration, and tests for cointegration using the bootstrap," Journal of Econometrics, Elsevier, vol. 110(2), pages 187-212, October.
  13. Zhongjun Qu, 2007. "Searching for cointegration in a dynamic system," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 580-604, November.
  14. Engle, Robert F. & Yoo, Byung Sam, 1987. "Forecasting and testing in co-integrated systems," Journal of Econometrics, Elsevier, vol. 35(1), pages 143-159, May.
  15. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  16. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  17. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
  18. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
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