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Testing for Cointegration in a Double-LSTR Framework

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  • Grote, Claudia
  • Sibbertsen, Philipp

Abstract

This paper investigates the finite-sample properties of the smooth transition-based cointegration test proposed by Kapetanios et al. (2006) when the data generating process under the alternative hypothesis is a globally stationary second order LSTR model. The provided procedure describes an application to long-run equilibrium relations involving real exchange rates with symmetric behaviour. We utilise the properties of the double LSTR transition function that features unit root behaviour within the inner regime and symmetric behaviour in the outer regimes. Hence, under the null hypothesis we imply no cointegration and globally stationary D-LSTR cointegration under the alternative. As a result of the identification problem the limiting distribution derived under the null hypothesis is non-standard. The Double LSTR is capable of producing three-regime TAR nonlinearity when the transition parameter tends to infinity as well as generating exponential-type nonlinearity that closely approximates ESTR nonlinearity. Therefore, we find that the Double LSTR error correction model has power against both of these alternatives.

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Bibliographic Info

Paper provided by Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät in its series Hannover Economic Papers (HEP) with number dp-514.

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Length: 14 pages
Date of creation: Jul 2013
Date of revision:
Handle: RePEc:han:dpaper:dp-514

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Keywords: Cointegration tests; LSTR; Monte carlo simulation; Nonlinear error correction;

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  1. Sollis, Robert, 2011. "Testing the unit root hypothesis against TAR nonlinearity using STAR-based tests," Economics Letters, Elsevier, vol. 112(1), pages 19-22, July.
  2. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  3. Enders, Walter & Granger, C. W. J., 1998. "Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Staff General Research Papers 1388, Iowa State University, Department of Economics.
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  6. Taylor, Alan M, 2001. "Potential Pitfalls for the Purchasing-Power-Parity Puzzle? Sampling and Specification Biases in Mean-Reversion Tests of the Law of One Price," Econometrica, Econometric Society, vol. 69(2), pages 473-98, March.
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  8. Siklos, P.L. & Granger, C.W.J., 1997. "Regime Sensitive Cointegration with an Application to Interest rate Parity," Working Papers 97-5, Wilfrid Laurier University, Department of Economics.
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  10. Taylor, Mark P. & Peel, David A., 2000. "Nonlinear adjustment, long-run equilibrium and exchange rate fundamentals," Journal of International Money and Finance, Elsevier, vol. 19(1), pages 33-53, February.
  11. Taylor, Mark P & Peel, David A & Sarno, Lucio, 2001. "Nonlinear Mean-Reversion in Real Exchange Rates: Toward a Solution to the Purchasing Power Parity Puzzles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1015-42, November.
  12. Bierens, Herman J. & Martins, Luis F., 2010. "Time-Varying Cointegration," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1453-1490, October.
  13. 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.
  14. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  15. Kaufmann, Hendrik & Kruse, Robinson & Sibbertsen, Philipp, 2012. "A simple specification procedure for the transition function in persistent nonlinear time series models," Hannover Economic Papers (HEP) dp-500, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
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