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Testing for Cointegration in Nonlinear STAR Error Correction Models

  • George Kapetanios

    ()

    (Queen Mary, University of London)

  • Yongcheol Shin

    (University of Edinburgh)

  • Andy Snell

    (University of Edinburgh)

In this paper we propose a new testing procedure to detect the presence of a cointegrating relationship that follows a globally stationary smooth transition autoregressive (STAR) process. We start from a general VAR model, embed the STAR error correction mechanism (ECM) and then derive the generalised nonlinear STAR error correction model. We provide two operational versions of the tests. Firstly, we obtain the associated nonlinear ECM-based test. Secondly, we generalise the well-known residual-based test for cointegration in linear models by Engle and Granger (1987) and obtain its nonlinear analogue. We derive the relevant asymptotic distributions of the proposed tests. We find via Monte Carlo simulation exercises that our proposed tests have much better power than the Engle and Granger test against the alternative of a globally stationary STAR cointegrating process. In an application to the price-dividend relationship, we also find that our test is able to find cointegration, whereas the linear-based tests fail to do so. Further analysis of impulse response functions of error correction terms (under the alternative) shows that the time taken to recover one half of a one standard deviation shock varies between five and twenty years, whereas the time taken to recover one half of a large shock varies between just 4 to 18 months. This clearly implies that data periods dominated by extreme volatility may display substantial mean reversion of the price-dividend relationship. By contrast this relationship may well look like a unit root when the underlying shocks take on smaller values.

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Paper provided by Queen Mary University of London, School of Economics and Finance in its series Working Papers with number 497.

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Date of creation: Jul 2003
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Handle: RePEc:qmw:qmwecw:wp497
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  1. van Dijk, D.J.C. & Terasvirta, T. & Franses, Ph.H.B.F., 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Research Papers EI 2000-23/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. Jeroen J.M. Kremers & Neil R. Ericsson & Juan J. Dolado, 1992. "The power of cointegration tests," International Finance Discussion Papers 431, Board of Governors of the Federal Reserve System (U.S.).
  3. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-79, August.
  4. Sarno, Lucio & Taylor, Mark P. & Chowdhury, Ibrahim, 2004. "Nonlinear dynamics in deviations from the law of one price: a broad-based empirical study," Journal of International Money and Finance, Elsevier, vol. 23(1), pages 1-25, February.
  5. Snell, Andy & Tonks, Ian, 1998. "Testing for asymmetric information and inventory control effects in market maker behaviour on the London Stock Exchange," Journal of Empirical Finance, Elsevier, vol. 5(1), pages 1-25, January.
  6. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
  7. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
  8. John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
  9. Nathan S. Balke & Thomas B. Fomby, 1992. "Threshold cointegration," Research Paper 9209, Federal Reserve Bank of Dallas.
    • 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.
  10. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  11. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, 07.
  12. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
  13. Sercu, Piet & Uppal, Raman & Van Hulle, Cynthia, 1995. " The Exchange Rate in the Presence of Transaction Costs: Implications for Tests of Purchasing Power Parity," Journal of Finance, American Finance Association, vol. 50(4), pages 1309-19, September.
  14. Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-11, July.
  15. Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(02), pages 301-340, April.
  16. M. Hashem Pesaran & Yongcheol Shin & Richard J. Smith, 2001. "Bounds testing approaches to the analysis of level relationships," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 289-326.
  17. Lo, Ming Chien & Zivot, Eric, 2001. "Threshold Cointegration And Nonlinear Adjustment To The Law Of One Price," Macroeconomic Dynamics, Cambridge University Press, vol. 5(04), pages 533-576, September.
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