IDEAS home Printed from https://ideas.repec.org/p/kud/kuiedp/1025.html
   My bibliography  Save this paper

Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models

Author

Listed:
  • Dennis Kristensen

    (Columbia University)

  • Anders Rahbek

    (Department of Economics, University of Copenhagen)

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 are considered. 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

  • Dennis Kristensen & Anders Rahbek, 2010. "Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models," Discussion Papers 10-25, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:1025
    as

    Download full text from publisher

    File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2010/1025.pdf/
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. de Jong, Robert M., 2001. "Nonlinear estimation using estimated cointegrating relations," Journal of Econometrics, Elsevier, vol. 101(1), pages 109-122, March.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Georg Keilbar & Yanfen Zhang, 2021. "On cointegration and cryptocurrency dynamics," Digital Finance, Springer, vol. 3(1), pages 1-23, March.
    6. 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.
    7. 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.
    8. She, Rui & Ling, Shiqing, 2020. "Inference in heavy-tailed vector error correction models," Journal of Econometrics, Elsevier, vol. 214(2), pages 433-450.
    9. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
    10. Andreas Hetland, 2018. "The Stochastic Stationary Root Model," Econometrics, MDPI, vol. 6(3), pages 1-33, August.
    11. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Novella Maugeri, 2014. "Some Pitfalls in Smooth Transition Models Estimation: A Monte Carlo Study," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 339-378, October.
    3. Jaebeom Kim & Masao Ogaki & Minseok Yang, 2007. "Structural Error Correction Models: A System Method for Linear Rational Expectations Models and an Application to an Exchange Rate Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(8), pages 2057-2075, December.
    4. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2017. "Correction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 883-883, April.
    5. Miller, Stephen M. & Martins, Luis Filipe & Gupta, Rangan, 2019. "A Time-Varying Approach Of The Us Welfare Cost Of Inflation," Macroeconomic Dynamics, Cambridge University Press, vol. 23(2), pages 775-797, March.
    6. repec:ipg:wpaper:2014-474 is not listed on IDEAS
    7. Seo Byeongseon, 2011. "Nonparametric Testing for Linearity in Cointegrated Error-Correction Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-28, March.
    8. Nedeljkovic, Milan, 2008. "Testing for Smooth Transition Nonlinearity in Adjustments of Cointegrating Systems," Economic Research Papers 269887, University of Warwick - Department of Economics.
    9. Zhou, Weilun & Gao, Jiti & Harris, David & Kew, Hsein, 2024. "Semi-parametric single-index predictive regression models with cointegrated regressors," Journal of Econometrics, Elsevier, vol. 238(1).
    10. Burton Hollifield & Robert A. Miller & Patrik Sandås, 2004. "Empirical Analysis of Limit Order Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 1027-1063.
    11. Nedeljkovic, Milan, 2008. "Testing for Smooth Transition Nonlinearity in Adjustments of Cointegrating Systems," The Warwick Economics Research Paper Series (TWERPS) 876, University of Warwick, Department of Economics.
    12. Robert M. deJong, 2000. "Nonlinear Minimization Estimators in the Presence of Cointegrating Relations," Econometric Society World Congress 2000 Contributed Papers 1651, Econometric Society.
    13. Nesmith Travis D & Jones Barry E, 2008. "Linear Cointegration of Nonlinear Time Series with an Application to Interest Rate Dynamics," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-18, March.
    14. Aguero, Jorge M., 2004. "Asymmetric Price Adjustments And Behavior Under Risk: Evidence From Peruvian Agricultural Markets," 2004 Annual meeting, August 1-4, Denver, CO 20394, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Jaebeom Kim & Masao Ogaki & Minseok Yang, 2003. "Structural Error Correction Models: Instrumental Variables Methods and an application to an exchange rate model," RCER Working Papers 502, University of Rochester - Center for Economic Research (RCER).
    16. 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.
    17. Bayer, Christian, 2006. "Investment dynamics with fixed capital adjustment cost and capital market imperfections," Journal of Monetary Economics, Elsevier, vol. 53(8), pages 1909-1947, November.
    18. Dennis Kristensen & Anders Rahbek, 2007. "Likelihood-Based Inference in Nonlinear Error-Correction Models," CREATES Research Papers 2007-38, Department of Economics and Business Economics, Aarhus University.
    19. Christis Katsouris, 2023. "Estimating Conditional Value-at-Risk with Nonstationary Quantile Predictive Regression Models," Papers 2311.08218, arXiv.org, revised Apr 2024.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kud:kuiedp:1025. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thomas Hoffmann (email available below). General contact details of provider: https://edirc.repec.org/data/okokudk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.