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Testing And Inference In Nonlinear Cointegrating Vector Error Correction Models

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  • Kristensen, Dennis
  • Rahbek, Anders

Abstract

We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new(uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full asymptotic theory for estimators and test statistics. The derived asymptotic results prove to be nonstandard compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. This complicates implementation of tests motivating the introduction of bootstrap versions that are simple to compute. A simulation study shows that the finite-sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes.

Suggested Citation

  • Kristensen, Dennis & Rahbek, Anders, 2013. "Testing And Inference In Nonlinear Cointegrating Vector Error Correction Models," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1238-1288, December.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:06:p:1238-1288_00
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    References listed on IDEAS

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    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. Georg Keilbar & Yanfen Zhang, 2021. "On cointegration and cryptocurrency dynamics," Digital Finance, Springer, vol. 3(1), pages 1-23, March.
    4. 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.
    5. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
    6. Popiel Michal Ksawery, 2017. "Interest rate pass-through: a nonlinear vector error-correction approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(5), pages 1-20, December.
    7. She, Rui & Ling, Shiqing, 2020. "Inference in heavy-tailed vector error correction models," Journal of Econometrics, Elsevier, vol. 214(2), pages 433-450.
    8. 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.
    9. Andreas Hetland, 2018. "The Stochastic Stationary Root Model," Econometrics, MDPI, vol. 6(3), pages 1-33, August.
    10. Chlibi Souhir & Jawadi Fredj & Sellami Mohamed, 2017. "Modeling threshold effects in stock price co-movements: a vector nonlinear cointegration approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(1), pages 47-63, February.
    11. Giuseppe Cavaliere & Anders Rahbek, 2019. "A Primer On Bootstrap Testing Of Hypotheses In Time Series Models: With An Application To Double Autoregressive Models," Discussion Papers 19-03, University of Copenhagen. Department of Economics.

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    More about this item

    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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