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Testing for Cointegration in Nonlinear STAR Error Correction Models

Author

Listed:
  • George Kapetanios

    () (Queen Mary, University of London)

  • Yongcheol Shin

    (University of Edinburgh)

  • Andy Snell

    (University of Edinburgh)

Abstract

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.

Suggested Citation

  • George Kapetanios & Yongcheol Shin & Andy Snell, 2003. "Testing for Cointegration in Nonlinear STAR Error Correction Models," Working Papers 497, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:wp497
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    File URL: http://www.econ.qmul.ac.uk/media/econ/research/workingpapers/archive/wp497.pdf
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    References listed on IDEAS

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    1. 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 627-645, August.
    2. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
    3. repec:bla:restud:v:57:y:1990:i:1:p:99-125 is not listed on IDEAS
    4. 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.
    5. Kremers, Jeroen J M & Ericsson, Neil R & Dolado, Juan J, 1992. "The Power of Cointegration Tests," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 325-348, August.
    6. 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.
    7. 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.
    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. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    10. 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.
    11. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    12. 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 1309-1319, September.
    13. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    14. Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(02), pages 301-340, April.
    15. 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 862-879, August.
    16. 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.
    17. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-1088, October.
    18. 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 304-311, July.
    19. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
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    Citations

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    Cited by:

    1. Tsangyao Chang & Yang-Cheng Lu, 2006. "Equity Diversification in Two Chinese Share Markets: Old Wine and New Bottle," Economics Bulletin, AccessEcon, vol. 7(4), pages 1-7.
    2. Zeynel Abidin Ozdemir, 2007. "The purchasing power parity hypothesis in Turkey: evidence from nonlinear STAR error correction models," Applied Economics Letters, Taylor & Francis Journals, vol. 15(4), pages 307-311.
    3. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    4. Liew, Venus Khim-Sen & Baharumshah, Ahmad Zubaidi & Habibullah, Muzafar Shah & Midi, Habshah, 2008. "Monetary exchange rate model: supportive evidence from nonlinear testing procedures," MPRA Paper 7293, University Library of Munich, Germany.
    5. J. Easaw J. & R. Golinelli, 2009. "Households Forming Inflation Expectations: Who Are the 'Active' and 'Passive' Learners?," Working Papers 675, Dipartimento Scienze Economiche, Universita' di Bologna.
    6. Gabriella Legrenzi & Costas Milas, 2012. "Fiscal Policy Sustainability, Economic Cycle and Financial Crises: The Case of the GIPS," Working Paper series 54_12, Rimini Centre for Economic Analysis.
    7. Daiki Maki, 2006. "Non-linear adjustment in the term structure of interest rates: a cointegration analysis in the non-linear STAR framework," Applied Financial Economics, Taylor & Francis Journals, vol. 16(17), pages 1301-1307.
    8. Jesús Gonzalo & Jean-Yves Pitarakis, 2006. "Threshold Effects in Cointegrating Relationships," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 813-833, December.
    9. Tsangyao Chang & Chien-Chung Nieh & Ching-Chun Wei, 2006. "Analysis of long-run benefits from international equity diversification between Taiwan and its major European trading partners: an empirical note," Applied Economics, Taylor & Francis Journals, vol. 38(19), pages 2277-2283.
    10. repec:rjr:romjef:v::y:2017:i:3:p:5-17 is not listed on IDEAS
    11. David G. McMillan & Mark E. Wohar, 2010. "Stock return predictability and dividend-price ratio: a nonlinear approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(4), pages 351-365.
    12. Chang, Tsangyao & Caudill, Steven B., 2006. "A note on the long-run benefits from international equity diversification for a Taiwan investor diversifying in the US equity market," International Review of Financial Analysis, Elsevier, vol. 15(1), pages 57-67.

    More about this item

    Keywords

    Unit roots; Globally stationary cointegrating processes; Nonlinear exponential smooth transition autoregressive error correction models; Monte Carlo simulations; Prices and dividends;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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