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Likelihood-Based Inference in Nonlinear Error-Correction Models

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  • Dennis Kristensen
  • Anders Rahbek

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties of the process in terms of stochastic and deter- ministic trends as well as stationary components. In particular, the behaviour of the cointegrating relations is described in terms of geo- metric ergodicity. Despite the fact that no deterministic terms are included, the process will have both stochastic trends and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study reveals that cointegration vectors and the shape of the adjust- ment are quite accurately estimated by maximum likelihood, while at the same time there is very little information about some of the individual parameters entering the adjustment function.

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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 2007-38.

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Length: 44
Date of creation: 19 Nov 2007
Date of revision:
Handle: RePEc:aah:create:2007-38

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

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  1. Hwan Seo, Myung, 2011. "Estimation Of Nonlinear Error Correction Models," Econometric Theory, Cambridge University Press, vol. 27(02), pages 201-234, April.
  2. Gonzalo, Jesùs & Pitarakis, Jean-Yves, 2005. "Threshold effects In multivariate error correction models," Discussion Paper Series In Economics And Econometrics 0501, Economics Division, School of Social Sciences, University of Southampton.
  3. 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.
  4. 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.
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  9. Jesus Gonzalo & Jean-Yves Pitarakis, 2006. "Threshold effects in cointegrating relationships," Economics Working Papers we20060621, Universidad Carlos III, Departamento de Economía.
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  14. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-80.
  15. 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.
  16. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
  17. Jensen, S ren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1203-1226, December.
  18. 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.
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Cited by:
  1. Marçal, Emerson Fernandes & Valls Pereira, Pedro L., 2012. "Evaluating the existence of structural change in the brazilian term structure of interest : evidence based on cointegration models with structural break," Textos para discussão 314, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  2. Nedeljkovic, Milan, 2008. "Testing for Smooth Transition Nonlinearity in Adjustments of Cointegrating Systems," The Warwick Economics Research Paper Series (TWERPS) 876, University of Warwick, Department of Economics.

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