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Testing for Cointegration in a System of Equations


  • Choi, In
  • Ahn, Byung Chul


This paper introduces various consistent tests for the null of cointegration against the alternative of noncointegration that can be applied to a system of equations as well as to a single equation. The tests are analogs of Choi and Ahn's (1993, Testing the Null of Stationarity for Multiple Time Series, working paper, The Ohio State University) multivariate tests for the null of stationarity and use Park's (1992, Econometrica 60, 119–143) canonical cointegrating regression (CCR) residuals to make the tests free of nuisance parameters in the limit. The asymptotic distributions of the tests are complex but expressed in unified manner by using standard vector Brownian motion. These distributions are tabulated by simulation for some practical cases. Furthermore, the rates of divergence of the tests are reported. Because there are methods for estimating cointegrating matrices other than CCR, it is illustrated for a model without time trends that the tests we introduce work exactly the same way in the limit when Phillips and Hansen's (1990, Review of Economic Studies 57, 99–125) fully modified ordinary least-squares (OLS) procedure is used. Also, is shown that difficulties arise when OLS residuals are used to formulate the tests. Small-scale simulation results are reported to examine the finite sample performance of the tests. The tests are shown to work reasonably wellin finite samples. In particular, it is illustrated that using the multivariate tests introduced in this paper can be a better testing strategy in terms of the finite sample size and power than applying univariate tests several times to each equation in a system of equations.

Suggested Citation

  • Choi, In & Ahn, Byung Chul, 1995. "Testing for Cointegration in a System of Equations," Econometric Theory, Cambridge University Press, vol. 11(5), pages 952-983, October.
  • Handle: RePEc:cup:etheor:v:11:y:1995:i:05:p:952-983_00

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    Cited by:

    1. Alan Bartley, William & Lee, Junsoo & Strazicich, Mark C., 2001. "Testing the null of cointegration in the presence of a structural break," Economics Letters, Elsevier, vol. 73(3), pages 315-323, December.
    2. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," Working Papers halshs-00564897, HAL.
    3. Won-Ki Seo, 2020. "Fully Modified Functional Principal Component Analysis for Cointegrated Functional Time Series," Papers 2011.12781,, revised Jun 2022.
    4. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, vol. 124(1), pages 187-201, January.
    5. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    6. Ho, Chun-Yu & Siu, Kam Wing, 2007. "A dynamic equilibrium of electricity consumption and GDP in Hong Kong: An empirical investigation," Energy Policy, Elsevier, vol. 35(4), pages 2507-2513, April.
    7. Josep Carrion-i-Silvestre & Andreu Sansó, 2007. "The KPSS test with two structural breaks," Spanish Economic Review, Springer;Spanish Economic Association, vol. 9(2), pages 105-127, June.
    8. Jansson, Michael, 2004. "Stationarity Testing With Covariates," Econometric Theory, Cambridge University Press, vol. 20(1), pages 56-94, February.
    9. Dilip M. Nachane, 2011. "Selected Problems in the Analysis of Nonstationary & Nonlinear Time Series," Journal of Quantitative Economics, The Indian Econometric Society, vol. 9(1), pages 1-17.
    10. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, vol. 186(1), pages 32-50.
    11. Choi, In, 2001. "Unit root tests for panel data," Journal of International Money and Finance, Elsevier, vol. 20(2), pages 249-272, April.
    12. In Choi & Hanbat Jeong, 2020. "Differencing versus nondifferencing in factor‐based forecasting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(6), pages 728-750, September.
    13. Choi, In & Chul Ahn, Byung, 1998. "Testing the null of stationarity for multiple time series," Journal of Econometrics, Elsevier, vol. 88(1), pages 41-77, November.
    14. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
    15. Josep Carrion-i-Silvestre & Andreu Sansó, 2006. "A guide to the computation of stationarity tests," Empirical Economics, Springer, vol. 31(2), pages 433-448, June.
    16. Alper Kara & Dilem Yıldırım & Gül İpek Tunç, 2021. "Market Efficiency In Non-Renewable Resource Markets: Evidence From Stationarity Tests With Structural Changes," ERC Working Papers 2103, ERC - Economic Research Center, Middle East Technical University, revised Apr 2021.
    17. Javier Fernandez-Macho, 2013. "A Test for the Null of Multiple Cointegrating Vectors," Economics Series Working Papers 657, University of Oxford, Department of Economics.

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