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First and second order non-linear cointegration models


  • Theis Lange

    () (Department of Economics, University of Copenhagen & CREATES)


This paper studies cointegration in non-linear error correction models characterized by discontinuous and regime-dependent error correction and variance specifications. In addition the models allow for autoregressive conditional heteroscedasticity (ARCH) type specifications of the variance. The regime process is assumed to depend on the lagged disequilibrium, as measured by the norm of linear stable or cointegrating relations. The main contributions of the paper are: i) conditions ensuring geometric ergodicity and nite second order moment of linear long run equilibrium relations and differenced observations, ii) a representation theorem similar to Granger's representations theorem and a functional central limit theorem for the common trends, iii) to establish that the usual reduced rank regression estimator of the cointegrating vector is consistent even in this highly extended model, and iv) asymptotic normality of the parameters for xed cointegration vector and regime parameters. Finally, an application of the model to US term structure data illustrates the empirical relevance of the model.

Suggested Citation

  • Theis Lange, 2009. "First and second order non-linear cointegration models," CREATES Research Papers 2009-04, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2009-04

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    Cited by:

    1. Stefano Puddu, 2013. "Real Sector and Banking System: Real and Feedback Effects. A Non-Linear VAR Approach," IRENE Working Papers 13-01, IRENE Institute of Economic Research.

    More about this item


    Cointegration; Non-linear adjustment; Regime switching; Multivariate ARCH.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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