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First and second order non-linear cointegration models

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Author Info

  • Theis Lange

    ()
    (Department of Economics, University of Copenhagen & CREATES)

Abstract

This paper studies cointegration in non-linear error correction models characterized by discontinuous and regime-dependent error correction and variance specifications. In addition the models allow for autoregressive conditional heteroscedasticity (ARCH) type specifications of the variance. The regime process is assumed to depend on the lagged disequilibrium, as measured by the norm of linear stable or cointegrating relations. The main contributions of the paper are: i) conditions ensuring geometric ergodicity and nite second order moment of linear long run equilibrium relations and differenced observations, ii) a representation theorem similar to Granger's representations theorem and a functional central limit theorem for the common trends, iii) to establish that the usual reduced rank regression estimator of the cointegrating vector is consistent even in this highly extended model, and iv) asymptotic normality of the parameters for xed cointegration vector and regime parameters. Finally, an application of the model to US term structure data illustrates the empirical relevance of the model.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-04.

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Length: 35
Date of creation: 10 Feb 2009
Date of revision:
Handle: RePEc:aah:create:2009-04

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Cointegration; Non-linear adjustment; Regime switching; Multivariate ARCH.;

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References

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  1. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Corradi, Valentina & Swanson, Norman R. & White, Halbert, 2000. "Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 39-73, May.
  3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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  6. Krolzig, Hans-Martin & Marcellino, Massimiliano & Mizon, Grayham E., 2000. "A Markov-switching vector equilibrium correction model of the UK labour market," Discussion Paper Series In Economics And Econometrics 0105, Economics Division, School of Social Sciences, University of Southampton.
  7. Akram, Q. Farooq & Nymoen, Ragnar, 2006. "Econometric modelling of slack and tight labour markets," Economic Modelling, Elsevier, vol. 23(4), pages 579-596, July.
  8. Saikkonen, Pentti, 2008. "Stability Of Regime Switching Error Correction Models Under Linear Cointegration," Econometric Theory, Cambridge University Press, vol. 24(01), pages 294-318, February.
  9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  10. Anderson, Heather M, 1997. "Transaction Costs and Non-linear Adjustment towards Equilibrium in the US Treasury Bill Market," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(4), pages 465-84, November.
  11. Catherine S. Forbes & Paul Kofman, 2000. "Bayesian Target Zones," Research Paper Series 32, Quantitative Finance Research Centre, University of Technology, Sydney.
  12. 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 1062-88, October.
  13. Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-26, February.
  14. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2006. "Testing For Cointegration In Nonlinear Smooth Transition Error Correction Models," Econometric Theory, Cambridge University Press, vol. 22(02), pages 279-303, April.
  15. Saikkonen, Pentti, 2005. "Stability results for nonlinear error correction models," Journal of Econometrics, Elsevier, vol. 127(1), pages 69-81, July.
  16. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
  17. Martin D. Evans & Karen K. Lewis, 1992. "Do Stationary Risk Premia Explain It All? Evidence from the Term Structure," Working Papers 92-11, New York University, Leonard N. Stern School of Business, Department of Economics.
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    • 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.
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  24. repec:cup:etheor:v:23:y:2007:i:04:p:761-766 is not listed on IDEAS
  25. Elias Tzavalis & Michael Wickens, . "The Rational Expectations Hypothesis of the Term Structure: reconciling the evidence," Discussion Papers 95/33, Department of Economics, University of York.
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Cited by:
  1. Stefano Puddu, 2013. "Real Sector and Banking System: Real and Feedback Effects. A Non-Linear VAR Approach," IRENE Working Papers 13-01, IRENE Institute of Economic Research.

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