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Likelihood-based inference for cointegration with nonlinear error-correction

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  • Kristensen, Dennis
  • Rahbek, Anders

Abstract

We consider a class of nonlinear vector error correction models where the transfer function (or loadings) of the stationary relationships 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 deterministic trends as well as stationary components. In particular, the behavior of the cointegrating relations is described in terms of geometric 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. Asymptotic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normality can be found. A simulation study reveals that cointegration vectors and the shape of the adjustment are quite accurately estimated by maximum likelihood. At the same time, there is very little information in data about some of the individual parameters entering the adjustment function if care is not taken in choosing a suitable specification.

Suggested Citation

  • Kristensen, Dennis & Rahbek, Anders, 2010. "Likelihood-based inference for cointegration with nonlinear error-correction," Journal of Econometrics, Elsevier, vol. 158(1), pages 78-94, September.
  • Handle: RePEc:eee:econom:v:158:y:2010:i:1:p:78-94
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    References listed on IDEAS

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    Cited by:

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    2. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.
    3. Dark, Jonathan, 2015. "Futures hedging with Markov switching vector error correction FIEGARCH and FIAPARCH," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 269-285.
    4. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    5. Berenguer-Rico, Vanessa & Nielsen, Bent, 2020. "Cumulated Sum Of Squares Statistics For Nonlinear And Nonstationary Regressions," Econometric Theory, Cambridge University Press, vol. 36(1), pages 1-47, February.

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