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residual-Based Tests for Cointegration in Models with Regime Shifts

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  • Allan w. Gregory
  • Bruce E. Hansen

Abstract

In this paper we examine tests for cointegration which allow for the possibility of regime shifts. We propose augmented Dickey-Fuller (ADF) and Phillips type tests designed to test the null of no cointegration against the alternative of cointegration in the presence of a possible regime shift. In particular we consider cases where the intercept and/or slope coefficients have a single break of unknown timing. A formal proof is provided for the limiting distributions of the various tests for the regime shift model (both a level and slope change). Critical values are calculated for the tests by simulation methods and a simple Monte Carlo experiment is conducted to evaluate finite sample performance. In the limited set of experiments, we find that the tests can detect cointegrating relations when there is a break in the intercept and/or slope coefficient. For these same experiments, the power of the conventional ADF test with no allowance for regime shifts falls sharply. As an illustration we test for structural breaks in the U.S. long-run money-demand equation using annual and quarterly data.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_862.pdf
File Function: First version 1992
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 862.

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Length: 48 pages
Date of creation: Nov 1992
Date of revision:
Handle: RePEc:qed:wpaper:862

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Keywords: level shift; regime shift; cointegration; Brownian motion;

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References

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  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
  2. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 10(3), pages 237-50, July.
  3. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-77, August.
  4. Vogelsang, T.I. & Perron, P., 1991. "Nonstationary and Level Shifts With An Application To Purchasing Power Parity," Papers, Princeton, Department of Economics - Econometric Research Program 359, Princeton, Department of Economics - Econometric Research Program.
  5. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  6. Gregory, Allan W. & Nason, James M. & Watt, David G., 1996. "Testing for structural breaks in cointegrated relationships," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 321-341.
  7. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 45-59, January.
  8. Phillips, P.C.B., 1988. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations," Econometric Theory, Cambridge University Press, vol. 4(03), pages 528-533, December.
  9. 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.
  10. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  11. Gregory, Allan W, 1994. "Testing for Cointegration in Linear Quadratic Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 12(3), pages 347-60, July.
  12. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(02), pages 213-221, June.
  13. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 25-44, January.
  14. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(4), pages 473-95, August.
  15. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, Econometric Society, vol. 60(4), pages 967-72, July.
  16. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers, Princeton, Department of Economics - Econometric Research Program 338, Princeton, Department of Economics - Econometric Research Program.
  17. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  18. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, Econometric Society, vol. 61(4), pages 783-820, July.
  19. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  20. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  21. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  22. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 277-301, March.
  23. Quintos, Carmela E & Phillips, Peter C B, 1993. "Parameter Constancy in Cointegrating Regressions," Empirical Economics, Springer, vol. 18(4), pages 675-706.
  24. Lucas, Robert E., 1988. "Money demand in the United States: A quantitative review," Carnegie-Rochester Conference Series on Public Policy, Elsevier, Elsevier, vol. 29(1), pages 137-167, January.
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