Nonlinear Equilibration, Cointegration and NEC Models

  • Gilles Dufrénot
  • Valérie Mignon


The relationships between economic variables in the long run can be investigated within a framework that is more general than the usual approach in terms of linear cointegration. A first question is whether there are economic reasons for introducing nonlinearities in the adjustment mechanism towards the long-term equilibrium. Clearly, many stylized facts can be evoked to account for the non-instantaneously adjusting behavior of economic variables. For instance, in financial markets prices are constrained to persistent short-run disequilibria due to information barriers, transaction costs, noise trading, market segmentation, etc. These imply a speed of adjustment of prices that is not constant through time and a nonlinear correcting mechanism. Although the concept of cointegration is quite new in the literature, much work has been done in the recent years on the topic.


Exchange Rate Lyapunov Exponent Unit Root Real Exchange Rate Unit Root Test 
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  1. Aparicio, F.M. and A. Escribano (1997). “Information-theoretic Analysis of Serial Dependence and Cointegration”, Working Paper, Universidad Carlos III, Madrid.Google Scholar
  2. Baffes, J., Elbadawi, I. and S. O’Connel (1997). “Single Equation of the Equilibrium Real Exchange Rate”, in Hinkle, L.E. and Montiel P.J., eds, Estimating Equilibrium Exchange Rates in Developing Countries, World Bank: Washington.Google Scholar
  3. Barnett, W.A. and P. Chen (1988). “Deterministic Chaos and Fractal Attractors as Tools for Nonparametric Dynamical Inferences”, Mathematical Computing and Modelling 10, 275–296.CrossRefGoogle Scholar
  4. Barron, A.R. (1991). “Universal Approximation Bounds for Superpositions of a Sigmoidal Function”, Technical Report 58, Department of Statistics, University of Illinois.Google Scholar
  5. Bierens, H.J. (1997). “Testing the Unit Root with Drift Hypothesis Against Nonlinear Trend Stationarity, with an Application to the US Price Level and Interest Rate”, Journal of Econometrics 81, 29–64.CrossRefGoogle Scholar
  6. Bierens, H.J. (1999). “Nonparametric Nonlinear Co-trending Analysis, with an Application to Interest and Inflation in the U.S.”, Working Paper, Tilburg University.Google Scholar
  7. Breiman, L. and J.H. Friedman (1985). “Estimating Transformations for Multiple Regression and Correlation”, Journal of the American Statistical Association 80, 614–619.Google Scholar
  8. Brock, W.A. (1986). “Distinguishing Random and Deterministic Systems: Abridged Version”, Journal of Economic Theory 40, 168–195.CrossRefGoogle Scholar
  9. Campbell, J.Y. and R.J. Shiller (1987). “Cointegration and Tests of Present Value Models”, Journal of Political Economy 5, 1062–1088.CrossRefGoogle Scholar
  10. Casdagli, M. (1989). “Nonlinear Prediction of Chaotic Time Series”, Physica D 35, 335–356.CrossRefGoogle Scholar
  11. Christie, W.G.and R.D. Huang (1994). “The Changing Functional Relation Between Stock Returns and Dividend Yields”, Journal of Empirical Finance 1, 161–191.CrossRefGoogle Scholar
  12. Clark, P.B. (1996). “Concepts of Equilibrium Exchange Rates”, Journal of International and Comparative Economics 20, 133–140.Google Scholar
  13. Clark, P.B. and R. McDonald (1998). “Exchange Rates and Economic Fundamental: A Methodological Comparison of BEERs and FEERs”, IMF Working Paper, 98 /67.Google Scholar
  14. Creedy, J. and L.V. Martin (1995). Chaos and Nonlinear Models in Economics, Edward Elgar: England.Google Scholar
  15. Creedy J., Lye, J. and L.V. Martin (1995). “Nonlinearities and the Long-run Real Exchange Distribution”, in Creedy, J. and L.V. Martin, eds, Chaos and Nonlinear Models in Economics, Edward Elgard: England.Google Scholar
  16. Cross R. (1995). The Natural Rate of Unemployment, Reflections on the 25 Years of the Hypothesis. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  17. Cybenko, G. (1989). “Approximations by Superpositions of a Sigmoidal Function”, Mathematics of Control, Signals and Systems 2, 303–314.CrossRefGoogle Scholar
  18. De Bandt, O. and F. Paolo Mongelli (2000). “Convergence of Fiscal Policies in the Euro Area”, Working Paper 20.Google Scholar
  19. De Grauwe, P.D. and H. Dewachter (1992). “Chaos in the Dornbusch Model of the Exchange Rate”, Kredit und Kapital 1, 27–54.Google Scholar
  20. Diba, B.T. and H.I. Grossman (1988). “Explosive Rational Bubbles in Stock Prices?”, American Economic Review 78, 520–529.Google Scholar
  21. Eckmann, J.P. and D. Ruelle (1985). “Ergodic Theory of Chaos and Strange Attractors”, Reviews of Modern Physics 57, 617–656.CrossRefGoogle Scholar
  22. Escribano, A. (1997). “Nonlinear Error-Correction: the Case of Money Demand in the U.K. (1878–1970)”, Working Paper, Universidad Carlos III, Madrid.Google Scholar
  23. Escribano, A. and O. Jorda (1996). “Improved Testing and Specification of Smooth Transition Regression Models”, Working Paper, Universidad Carlos III, Madrid.Google Scholar
  24. Escribano, A. and S. Mira (1996). “Nonlinear Cointegration and Nonlinear Error-Correction”, Working Paper, Universidad Carlos III, Madrid.Google Scholar
  25. Escribano, A. and S. Mira (1997). “Nonlinear Cointegration with Mixing Errors”, Working Paper, Universidad Carlos III, Madrid.Google Scholar
  26. Escribano, A. and S. Mira (1998). “Nonlinear Error-Correction Models”, Working Paper, Universidad Carlos III, Madrid.Google Scholar
  27. Evans, G.W. (1991). “Pitfalls in Testing for Explosive Bubbles in Asset Prices”, American Economic Review 4, 922–930.Google Scholar
  28. Farmer, J.D., Ott, E. and J.A. Yorke (1983). “The Dimension of Chaotic Attractors”, Physica 7D, 153–180.Google Scholar
  29. Flood, R.P. and N.P. Marion (1998). “Perspectives on the Recent Currency Crisis Literature”, NBER Working Paper 6380.Google Scholar
  30. Goldfeld, S.M. and R.E. Quandt (1972). Nonlinear Methods in Econometrics. North Holland Publ. Co., 5–9.Google Scholar
  31. Granger, C.W.J. and J. Hallman (1991). “Long-memory Series with Attractors”, Oxford Bulletin of Economics and Statistics 53, 11–26.CrossRefGoogle Scholar
  32. Guckenheimer, J. and P. Holmes (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer Verlag: New York.Google Scholar
  33. Haken, H. (1983). Synergetics. An Introduction, Springer-Verlag: Berlin-HeidelbergNew York.Google Scholar
  34. Hardie, W. and O. Linton (1994). “Applied Nonparametric Methods”, Handbook of Econometrics Vol. IV, ch.38, 2297–2339.Google Scholar
  35. Hornik, K., Stinchcombe, M. and H. White (1989). “Multi-layer feedforward networks are universal approximators”, Neural Networks 2, 359–366.CrossRefGoogle Scholar
  36. Ikeda, S. and A. Shibata (1995). “Fundamental Uncertainty, Bubbles, and Exchange Rate Dynamics”, Journal of International Economics 38, 199–222.CrossRefGoogle Scholar
  37. Isard, P. and H. Faruqee (1998). “Exchange Rate Assessment: Some Recent Extensions and Application of the Macroeconomic Balance Approach”, Occasional Paper, IMF, Washington.Google Scholar
  38. Kantz, H. (1994). “A Robust Method to Estimate the Maximal Lyapunov Exponent of a Time Series”, Physical Letters A, 185.Google Scholar
  39. Kantz, H. and T. Schreiber (1997). Nonlinear Time Series Analysis. Cambridge Nonlinear Science Series 7, Cambridge University Press.Google Scholar
  40. Krugman, P. (1991). “Target Zones and Exchange Rate Dynamics”, Quarterly Journal of Economics 106, 669–682.CrossRefGoogle Scholar
  41. Krugman, P. and M. Miller (1993). “Why Have a Target Zone?”, Carnegie-Rochester Conference Series on Public Policy 38, 279–314.CrossRefGoogle Scholar
  42. Kuan, C.M. and T. Liu (1995). “Forecasting Exchange Rates Using Feedforward and Recurrent Neural Networks”, Journal of Applied Econometrics 10, 347–364.CrossRefGoogle Scholar
  43. Kuan, C.M. and H. White (1990). “Predicting Appliance Ownership using Logit, Neural Network and Regression Tree Models”, BEBR Working Paper 90–1647, College of Commerce, University of Illinois.Google Scholar
  44. Lorenz, H.W. (1989). Nonlinear Dynamical Economics and Chaotic Motion. Springer Verlag: New-York.Google Scholar
  45. Ma, Y. and A. Kanas (2000). “Testing for a Nonlinear Relationship among Fundamentals and Exchange Rates in the ERM”, Journal of International Money and Finance 19, 135–152.CrossRefGoogle Scholar
  46. Mc Donald, R., Ben Salem, M. and F. Bec (1999). “Real Exchange Rates and Real Interest Rates: A Nonlinear Perspective”, Thema Working Paper, University of Paris X.Google Scholar
  47. Markellos, R.N. (1997). “Nonlinear Equilibrium Dynamics”, Economic Research Paper, Loughborough University, 97/16.Google Scholar
  48. Mathieu, L. (1996). Séries chaotiques et analyse économique, Doctoral Thesis, University of Paris X.Google Scholar
  49. Medio, A. (1984). “Synergetics and Dynamic Economic Models”, in Goodwin, R.M., Kruger, M. and A. Vercelli, eds, Nonlinear Models of Fluctuating Growth. Springer Verlag: Berlin-Heidelberg-New York.Google Scholar
  50. Meese, R.A. and A.K. Rose (1991). “An Empirical Assessment of Nonlinearities in Models of Exchange Rate Determination”, Review of Economic Studies 58, 603619.Google Scholar
  51. Mignon, V. (1998). Marchés financiers et modélisation des rentabilités boursières, Economica: Paris.Google Scholar
  52. Mira, S. (1996). Modelos Econometricos Dinamicos No Lineares con Tendencias Estocasticas, PhD. Dissertation, Universidad Carlos III, Madrid.Google Scholar
  53. Mizrach, B. (1992). “Multivariate Nearest-neighbour Forecasts of EMS Exchange Rates”, Journal of Applied Econometrics 7, 151–163.CrossRefGoogle Scholar
  54. Mukai, H. (1979). “Readily Implementable Conjugate Gradient Methods”, Mathematical Programming 17, 298–319.CrossRefGoogle Scholar
  55. Oren, S.S. and D.G. Luenberger (1974). “Self Scaling Variable Metric Algorithms, Part P”, Management Science 20.Google Scholar
  56. Péguin-Feissolle, A. and T. Teräsvirta (2001). “Causality Tests in a Nonlinear Framework”, Working paper, Stockholm School of Economics, Stockholm.Google Scholar
  57. Phillips, P.C. and S.N. Durlauf (1986). “Multiple Time Series Regression with Integrated Processes”, Review of Economic Studies 4, 473–495.CrossRefGoogle Scholar
  58. Powell, M.J.D. (1971). “Recent Advances Unconstrained Optimization”, Mathematical Programming 1, 26–57.CrossRefGoogle Scholar
  59. Rosenstein, M.T., Collins, J.J. and C.J. De Luca (1993). “A Practical Method for Calculating the Largest Exponent from Small Data Sets”, Physica D, 65.Google Scholar
  60. Schinasi, G.J. and P.A. Swamy (1989). “The Out-of-sample Forecasting Performance of Exchange Rate Models when Coefficients are Allowed to Change”, Journal of International Money and Finance 8, 375–390.CrossRefGoogle Scholar
  61. Stark, J., Broomhead, D.S., Davies, M.E. and J. Huke (1996). “Takens Embedding Theorems for Forced and Stochastic Systems”, World Congress of Nonlinear Analyst, Athens, Greece.Google Scholar
  62. Stein, J.L. (1995). Fundamental Determinants of Exchange Rates,Oxford University Press.Google Scholar
  63. Takens, F. (1981). “Detecting Strange Attractors in Turbulence”, in Rand, D. and L. Young, eds, Dynamical Systems and Turbulence, Springer Verlag: Berlin-HeidelbergNew York.Google Scholar
  64. Terasvirta, T. (1994). “Specification, Estimation and Evaluation of Smooth Transition Autoregressive Models”, Journal of the American Statistical Association 425, 208–218.Google Scholar
  65. Varian, H.R. (1979). “Catastrophe Theory and the Business Cycle”, Economic Inquiry 17, 14–28.CrossRefGoogle Scholar
  66. Weidlich, W. and G. Haag (1983). Concepts and Models of a Quantitative Sociology. Springer-Verlag: Berlin-Heidelberg-New York.CrossRefGoogle Scholar
  67. White, H. (1988). “Economic Prediction using Neural Networks: The Case of IBM Stock Prices”, in Proceedings of the IEEE Second International Conference on Neural Networks II, 451–458.CrossRefGoogle Scholar
  68. White, H. (1989). “Some Asymptotic Results for Learning in Single hidden-layer Feedforward Network Models”, Journal of the American Statistical Association 84, 1003–1013.CrossRefGoogle Scholar
  69. Williamson, J. (1994). Estimating Equilibrium Exchange Rates,Institute for International Economics.Google Scholar
  70. Woodcock, A.E.R., and M. Davis (1979). Catastrophe Theory. Penguin: LondonGoogle Scholar
  71. Yuhn, K.H. (1996). “Stock Price Volatility: Tests for Linear and Nonlinear Cointegration in the Present Value Model of Stock Prices”, Applied Financial Economics 6, 487–494.CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Gilles Dufrénot
    • 1
    • 2
  • Valérie Mignon
    • 3
  1. 1.ERUDITEUniversity of Paris 12France
  2. 2.GREQUAM-CNRSUniversity of MarseilleFrance
  3. 3.MODEMUniversity of Paris 10France

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