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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.

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  • 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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    2. Heejoon Han & Dennis Kristensen, 2014. "Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 416-429, July.
    3. 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.
    4. James A. Duffy & Sophocles Mavroeidis, 2024. "Common Trends and Long-Run Identification in Nonlinear Structural VARs," Papers 2404.05349, arXiv.org, revised Sep 2024.
    5. Georg Keilbar & Yanfen Zhang, 2021. "On cointegration and cryptocurrency dynamics," Digital Finance, Springer, vol. 3(1), pages 1-23, March.
    6. Skrobotov, Anton, 2021. "Structural breaks in cointegration models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 63, pages 117-141.
    7. 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.
    8. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    9. Escribano, Alvaro & Peña, Daniel & Ruiz, Esther, 2021. "30 years of cointegration and dynamic factor models forecasting and its future with big data: Editorial," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1333-1337.
    10. Cavaliere, Giuseppe & Mikosch, Thomas & Rahbek, Anders & Vilandt, Frederik, 2024. "Tail behavior of ACD models and consequences for likelihood-based estimation," Journal of Econometrics, Elsevier, vol. 238(2).
    11. Kazuhiko Hayakawa & M. Hashem Pesaran & L. Vanessa Smith, 2023. "Short T dynamic panel data models with individual, time and interactive effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(6), pages 940-967, September.
    12. Vanessa Berenguer-Rico & Bent Nielsen, 2015. "Cumulated sum of squares statistics for non-linear and non-stationary regressions," Economics Papers 2015-W09, Economics Group, Nuffield College, University of Oxford.
    13. Andreas Hetland, 2018. "The Stochastic Stationary Root Model," Econometrics, MDPI, vol. 6(3), pages 1-33, August.
    14. James A. Duffy & Sophocles Mavroeidis & Sam Wycherley, 2022. "Cointegration with Occasionally Binding Constraints," Papers 2211.09604, arXiv.org, revised Jul 2023.

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