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Testing for Linear Cointegration Against Smooth-Transition Cointegration

  • Li, Dao

    ()

    (School of Technology and Business Studies)

  • He, Changli

    ()

    (School of Technology and Business Studies)

Registered author(s):

    This paper studies a smooth-transition (ST) type cointegration. The proposed ST cointegration allows for regime switching structure in a cointegrated system, and nests the linear cointegration developed by Engle and Granger (1987) and the threshold cointe- gration studied by Balke and Fomby (1997). Based on a class of vector ST cointegrating regression models, we develop F-type tests to examine linear cointegration against ST cointegration. The null asymptotic distributions of the tests with choosing various sta- tionary transition variables are derived. Finite-sample distributions of those tests are studied by Monto Carlo simulation. The small-sample performance of the tests are also included and it is shown that our F-type tests have a better power when the system contains a ST cointegration than that when the system is linearly cointegrated. Two empirical examples for the purchasing power parity (PPP) data are illustrated by apply- ing the testing procedures in this paper. It is found that, for each of them, there is no linear cointegration in the system, but there exits a ST cointegration in the system.

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    File URL: http://www.oru.se/PageFiles/36235/WP%206%202012%20-%20rev.pdf
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    Paper provided by Örebro University, School of Business in its series Working Papers with number 2012:6.

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    Length: 55 pages
    Date of creation: 13 Feb 2012
    Date of revision:
    Handle: RePEc:hhs:oruesi:2012_006
    Contact details of provider: Postal: Örebro University School of Business, SE - 701 82 ÖREBRO, Sweden
    Phone: 019-30 30 00
    Fax: 019-33 25 46
    Web page: http://www.oru.se/Institutioner/Handelshogskolan-vid-Orebro-universitet/

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    1. Perron, P., 1989. "Testing For A Unit Root In A Time Series With A Changing Mean," Papers 347, Princeton, Department of Economics - Econometric Research Program.
    2. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    3. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
    4. Baillie, Richard T. & Selover, David D., 1987. "Cointegration and models of exchange rate determination," International Journal of Forecasting, Elsevier, vol. 3(1), pages 43-51.
    5. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
    6. He, Changli & Sandberg, Rickard, 2005. "Testing Parameter Constancy in Unit Root Autoregressive Models Against Continuous Change," SSE/EFI Working Paper Series in Economics and Finance 579, Stockholm School of Economics, revised 08 Feb 2005.
    7. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
    8. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
    9. In Choi & Pentti Saikkonen, 2004. "Testing linearity in cointegrating smooth transition regressions," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 341-365, December.
    10. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-45, August.
    11. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
    12. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
    13. Corbae, Dean & Ouliaris, Sam, 1988. "Cointegration and Tests of Purchasing Power Parity," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 508-11, August.
    14. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
    15. Peter C.B. Phillips & Joon Y. Park, 1998. "Asymptotics for Nonlinear Transformations of Integrated Time Series," Cowles Foundation Discussion Papers 1182, Cowles Foundation for Research in Economics, Yale University.
    16. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University.
    17. He, Changli & Sandberg, Rickard, 2005. "Testing for Unit Roots in Nonlinear Dynamic Heterogeneous Panels," SSE/EFI Working Paper Series in Economics and Finance 582, Stockholm School of Economics.
    18. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
    19. Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(02), pages 301-340, April.
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