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Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests

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  • Wright, Jonathan H

Abstract

Standard methods for inference in cointegrating systems require all the variables to have exact unit roots and are not at all robust even to slight violations of this condition. In this article, I consider an alternative approach to inference in a cointegrating system. This involves testing the hypothesis that a cointegrating vector takes on a specified value by testing for the stationarity of the associated residual. Confidence sets for the cointegrating vector can be constructed by exploiting the equivalence between tests and confidence sets. This method has the advantage that it remains valid even if the regressors have roots that are not exactly equal to unity.

Suggested Citation

  • Wright, Jonathan H, 2000. "Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 211-222, April.
    • Handle: RePEc:bes:jnlbes:v:18:y:2000:i:2:p:211-22
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    Cited by:

    1. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    2. Erik Hjalmarsson & Pär Österholm, 2010. "Testing for cointegration using the Johansen methodology when variables are near-integrated: size distortions and partial remedies," Empirical Economics, Springer, vol. 39(1), pages 51-76, August.
    3. Benati, Luca & Lucas, Robert E. & Nicolini, Juan Pablo & Weber, Warren, 2021. "International evidence on long-run money demand," Journal of Monetary Economics, Elsevier, vol. 117(C), pages 43-63.
    4. Ulrich K. Müller & Mark W. Watson, 2024. "Spatial Unit Roots and Spurious Regression," Econometrica, Econometric Society, vol. 92(5), pages 1661-1695, September.
    5. Sophocles N. Brissimis & Petros M. Migiakis, 2016. "Inflation persistence, learning dynamics and the rationality of inflation expectations," Empirical Economics, Springer, vol. 51(3), pages 963-979, November.
    6. Maynard, Alex & Shimotsu, Katsumi, 2009. "Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence," Econometric Theory, Cambridge University Press, vol. 25(1), pages 63-116, February.
    7. Müller, Ulrich K. & Watson, Mark W., 2013. "Low-frequency robust cointegration testing," Journal of Econometrics, Elsevier, vol. 174(2), pages 66-81.
    8. Kurt Graden Lunsford, 2023. "Business Cycles and Low-Frequency Fluctuations in the US Unemployment Rate," Working Papers 23-19, Federal Reserve Bank of Cleveland.
    9. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    10. Jean-Thomas Bernard & Ba Chu & Lynda Khalaf & Marcel Voia, 2019. "Non-Standard Confidence Sets for Ratios and Tipping Points with Applications to Dynamic Panel Data," Annals of Economics and Statistics, GENES, issue 134, pages 79-108.
    11. M. Shahe Emran & Forhad Shilpi & M. Imam Alam, 2007. "Economic liberalization and price response of aggregate private investment: time series evidence from India," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 40(3), pages 914-934, August.
    12. Benati, Luca, 2020. "Money velocity and the natural rate of interest," Journal of Monetary Economics, Elsevier, vol. 116(C), pages 117-134.
    13. Nikitas Pittis & Christina Christou & Sarantis Kalyvitis & Christis Hassapis, 2009. "Long‐Run PPP under the Presence of Near‐to‐Unit Roots: The Case of the British Pound–US Dollar Rate," Review of International Economics, Wiley Blackwell, vol. 17(1), pages 144-155, February.
    14. Erik Hjalmarsson & Pär Österholm, 2007. "A residual-based cointegration test for near unit root variables," International Finance Discussion Papers 907, Board of Governors of the Federal Reserve System (U.S.).
    15. Moreira, Marcelo J. & Mourão, Rafael & Moreira, Humberto Ataíde, 2016. "A critical value function approach, with an application to persistent time-series," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 778, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    16. Jonathan H. Wright, 1999. "A simple approach to robust inference in a cointegrating system," International Finance Discussion Papers 654, Board of Governors of the Federal Reserve System (U.S.).
    17. Kang, Heejoon, 2008. "The cointegration relationships among G-7 foreign exchange rates," International Review of Financial Analysis, Elsevier, vol. 17(3), pages 446-460, June.
    18. Khalaf, Lynda & Urga, Giovanni, 2014. "Identification robust inference in cointegrating regressions," Journal of Econometrics, Elsevier, vol. 182(2), pages 385-396.

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