IDEAS home Printed from
   My bibliography  Save this article

Tests For Nonlinear Cointegration


  • Choi, In
  • Saikkonen, Pentti


This paper develops tests for the null hypothesis of cointegration in the nonlinear regression model with I(1) variables. The test statistics we use in this paper are Kwiatkowski, Phillips, Schmidt, and Shin’s (1992; KPSS hereafter) tests for the null of stationarity, though using other kinds of tests is also possible. The tests are shown to depend on the limiting distributions of the estimators and parameters of the nonlinear model when they use full-sample residuals from the nonlinear least squares and nonlinear leads-and-lags regressions. This feature makes it difficult to use them in practice. As a remedy, this paper develops tests using subsamples of the regression residuals. For these tests, first, the nonlinear least squares and nonlinear leads-and-lags regressions are run and residuals are calculated. Second, the KPSS tests are applied using subresiduals of size b. As long as b/T → 0 as T → ∞, where T is the sample size, the tests using the subresiduals have limiting distributions that are not affected by the limiting distributions of the full-sample estimators and the parameters of the model. Third, the Bonferroni procedure is used for a selected number of the subresidual-based tests. Monte Carlo simulation shows that the tests work reasonably well in finite samples for polynomial and smooth transition regression models when the block size is chosen by the minimum volatility rule. In particular, the subresidual-based tests using the leads-and-lags regression residuals appear to be promising for empirical work. An empirical example studying the U.S. money demand equation illustrates the use of the tests.

Suggested Citation

  • Choi, In & Saikkonen, Pentti, 2010. "Tests For Nonlinear Cointegration," Econometric Theory, Cambridge University Press, vol. 26(3), pages 682-709, June.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:03:p:682-709_99

    Download full text from publisher

    File URL:
    File Function: link to article abstract page
    Download Restriction: no


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Shota Moriwaki, 2017. "Sustainable Development in Four East Asian Countries' Agricultural Sectors Post-World War II: Measuring Nutrient Balance and Estimating the Environmental Kuznets Curve," Asia and the Pacific Policy Studies, Wiley Blackwell, vol. 4(3), pages 467-483, September.
    2. Yicong Lin & Hanno Reuvers, 2019. "Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve," Papers 1908.02552,, revised Aug 2020.
    3. Chen, Haiqiang, 2015. "Robust Estimation And Inference For Threshold Models With Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 31(4), pages 778-810, August.
    4. Kander, Astrid & Stern, David I., 2014. "Economic growth and the transition from traditional to modern energy in Sweden," Energy Economics, Elsevier, vol. 46(C), pages 56-65.
    5. de Mello Luiz & Moccero Diego & Mogliani Matteo, 2013. "Do Latin American Central Bankers Behave Non-Linearly? The Experiences of Brazil, Chile, Colombia and Mexico," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 141-165, April.
    6. Götz, Linde & Qiu, Feng & Gervais, Jean-Philippe & Glauben, Thomas, 2013. "Export Restrictions and Multiple Spatial Price Equilibria: Export Quotas for Wheat in Ukraine," 53rd Annual Conference, Berlin, Germany, September 25-27, 2013 156135, German Association of Agricultural Economists (GEWISOLA).
    7. Sequeira, Tiago Neves & Gil, Pedro Mazeda & Afonso, Oscar, 2018. "Endogenous growth and entropy," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 100-120.
    8. Mikael Juselius & Moshe Kim, 2017. "Sustainable Financial Obligations and Crisis Cycles," Econometrics, MDPI, Open Access Journal, vol. 5(2), pages 1-23, June.
    9. Stern, David I. & Enflo, Kerstin, 2013. "Causality between energy and output in the long-run," Energy Economics, Elsevier, vol. 39(C), pages 135-146.
    10. Yicong Lin & Hanno Reuvers, 2020. "Cointegrating Polynomial Regressions with Power Law Trends: A New Angle on the Environmental Kuznets Curve," Papers 2009.02262,
    11. Andrea Vaona, 2015. "Anomalous empirical evidence on money long-run super-neutrality and the vertical long-run Phillips curve," Working Papers 17/2015, University of Verona, Department of Economics.
    12. Suphi Sen & Bertrand Melenberg & Herman R. J. Vollebergh, 2016. "Identification and Estimation of the Environmental Kuznets Curve: Pairwise Differencing to Deal with Nonlinearity and Nonstationarity," CESifo Working Paper Series 5837, CESifo.
    13. repec:wyi:journl:002203 is not listed on IDEAS
    14. Richard Green and Nicholas Vasilakos, 2012. "Storing Wind for a Rainy Day: What Kind of Electricity Does Denmark Export?," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    15. Beenstock, Michael & Reingewertz, Yaniv & Paldor, Nathan, 2016. "Testing the historic tracking of climate models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1234-1246.
    16. Sephton, Peter & Mann, Janelle, 2013. "Further evidence of an Environmental Kuznets Curve in Spain," Energy Economics, Elsevier, vol. 36(C), pages 177-181.
    17. Gu, Jingping & Liang, Zhongwen, 2014. "Testing cointegration relationship in a semiparametric varying coefficient model," Journal of Econometrics, Elsevier, vol. 178(P1), pages 57-70.
    18. Chan, Nigel & Wang, Qiying, 2015. "Nonlinear regressions with nonstationary time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 182-195.
    19. David I. Stern and Astrid Kander, 2012. "The Role of Energy in the Industrial Revolution and Modern Economic Growth," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    20. Berenguer-Rico, Vanessa & Nielsen, Bent, 2020. "Cumulated Sum Of Squares Statistics For Nonlinear And Nonstationary Regressions," Econometric Theory, Cambridge University Press, vol. 36(1), pages 1-47, February.
    21. Liew, Venus Khim-Sen & Ling, Tai-Hu & Chia, Ricky Chee-Jiun & Yoon, Gawon, 2012. "On the application of the rank tests for nonlinear cointegration to PPP: The case of Papua New Guinea," Economic Modelling, Elsevier, vol. 29(2), pages 326-332.
    22. Michael L. Polemis & Mike G. Tsionas, 2019. "Bayesian nonlinear panel cointegration: an empirical application to the EKC hypothesis," Letters in Spatial and Resource Sciences, Springer, vol. 12(2), pages 113-120, August.
    23. Gotz, Linde & Qiu, Feng & Gervais, Jean-Philippe & Glauben, Thomas, 2012. "Export Restrictions And Multiple Spatial Price Equilibria When International Prices Spike: Export Quotas For Wheat In Ukraine," 2012: New Rules of Trade? December 2012, San Diego, California 143179, International Agricultural Trade Research Consortium.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:26:y:2010:i:03:p:682-709_99. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.