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Nonlinear cointegration and nonlinear error correction

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  • Escribano, Álvaro
  • Mira, Santiago

Abstract

The relationships between stochastic trending variables given by the concepts of cointegration and error correction (EC) are well characterized in a linear context, but the extension to a nonlinear context is still a challenge. Few extensions of the linear framework were developed in the context of linear cointegration but nonlinear error correction (NEC) models, and even in this context, there are still many open questions. The theoretical framework is not well developed at this moment and only particular cases have been discussed empirically. In this paper we propose a statistical framework that allow us to address those issues. First, we generalize the notion of integration to the nonlinear case. As a result a generalization of cointegration is feasible, and also a formal definition of NEC models. Within this framework we analyze the nonlinear least squares (NLS) estimation of nonlinear cointegration relations and the extension of the two-step estimation procedures of Engle and Granger (1987) for NEC models. Finally, we discuss a generalization of Granger Representation Theorem to the nonlinear case and discuss the properties of the onestep (NLS) procedure to estimate NEC models.

Suggested Citation

  • Escribano, Álvaro & Mira, Santiago, 1996. "Nonlinear cointegration and nonlinear error correction," DES - Working Papers. Statistics and Econometrics. WS 4546, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:4546
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    References listed on IDEAS

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    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
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    7. Escribano, A., 1987. "Error-correction systems: nonlinear adjustments to linear long-run relationships," LIDAM Discussion Papers CORE 1987030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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    11. Mira, Santiago & Escribano, Álvaro, 1995. "Nonlinear time series models: consistency and asymptotic normality of nls under new conditions," DES - Working Papers. Statistics and Econometrics. WS 6202, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
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    Cited by:

    1. van Dijk, D.J.C. & Franses, Ph.H.B.F., 1997. "Nonlinear Error-Correction Models for Interest Rates in The Netherlands," Econometric Institute Research Papers EI 9704-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Ben Kaabia, Monia & Gil, Jose Maria, 2005. "Asymetric Price Transmission in the Spanish Lamb Sector," 2005 International Congress, August 23-27, 2005, Copenhagen, Denmark 24631, European Association of Agricultural Economists.
    3. Isabella Procidano & Margherita Gerolimetto & Silio Rigatti Luchini, 2006. "Dynamic cointegration and relevant vector machine: the relationship between gold and silver," Computing in Economics and Finance 2006 380, Society for Computational Economics.
    4. George Kapetanios, 2003. "Threshold models for trended time series," Empirical Economics, Springer, vol. 28(4), pages 687-707, November.
    5. Peel, David & Davidson, James, 1998. "A non-linear error correction mechanism based on the bilinear model1," Economics Letters, Elsevier, vol. 58(2), pages 165-170, February.
    6. Mustapha Baghli, 2004. "Modelling the FF/MM rate by threshold cointegration analysis," Applied Economics, Taylor & Francis Journals, vol. 36(6), pages 533-548.
    7. Monia Ben-Kaabia & José M. Gil & Mehrez Ameur, 2005. "Vertical integration and non-linear price adjustments: The Spanish poultry sector," Agribusiness, John Wiley & Sons, Ltd., vol. 21(2), pages 253-271.
    8. Aparicio F. M. & Escribano A., 1998. "Information-Theoretic Analysis of Serial Dependence and Cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(3), pages 1-24, October.
    9. Dilip M. Nachane, 2011. "Selected Problems in the Analysis of Nonstationary & Nonlinear Time Series," Journal of Quantitative Economics, The Indian Econometric Society, vol. 9(1), pages 1-17.
    10. Junttila, Juha & Korhonen, Marko, 2011. "Nonlinearity and time-variation in the monetary model of exchange rates," Journal of Macroeconomics, Elsevier, vol. 33(2), pages 288-302, June.

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