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Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models

Author

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  • Dennis Kristensen

    () (Dep. of Economics, Columbia University and CREATES)

  • Anders Rahbek

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

Abstract

In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing for linearity is of particular interest as parameters of non-linear components vanish under the null. To solve the latter type of testing, we use the so-called sup tests, which here requires development of new (uniform) weak convergence results. These results are potentially useful in general for analysis of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. With respect to testing, this makes implementation of testing involved, and bootstrap versions of the tests are proposed in order to facilitate their usage. The asymptotic results regarding the QML estimators extend results in Kristensen and Rahbek (2010, Journal of Econometrics) where symmetric non-linear error correction considered. A simulation study shows that the fi?nite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes.

Suggested Citation

  • Dennis Kristensen & Anders Rahbek, 2010. "Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models," CREATES Research Papers 2010-68, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-68
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    References listed on IDEAS

    as
    1. de Jong, Robert M., 2002. "Nonlinear minimization estimators in the presence of cointegrating relations," Journal of Econometrics, Elsevier, vol. 110(2), pages 241-259, October.
    2. de Jong, Robert M., 2001. "Nonlinear estimation using estimated cointegrating relations," Journal of Econometrics, Elsevier, vol. 101(1), pages 109-122, March.
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    Cited by:

    1. 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.
    2. Boswijk, H. Peter & Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2016. "Inference on co-integration parameters in heteroskedastic vector autoregressions," Journal of Econometrics, Elsevier, vol. 192(1), pages 64-85.
    3. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
    4. Michal Popiel, 2016. "Interest rate pass-through: a nonlinear vector error-correction approach," Working Papers 1352, Queen's University, Department of Economics.

    More about this item

    Keywords

    Nonlinear error correction; cointegration; testing nonlinearity; nonlinear time series; sup tests; vanishing parameters; testing.;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - 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

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