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Testing the null of cointegration with a structural break: optimal kernel and bandwidth selection

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  • Alexander Ludwig

    () (TU Dresden)

Abstract

Structural breaks in relationships between macroeconomic and financial time series are likely a result of financial crises or local reforms. If such structural breaks exist, cointegration tests have to take them into account. Arai and Kurozumi (2007), Carrion-i-Silvestre and Sanso (2006) and Kejriwal (2008) propose a test for the null of cointegration with structural breaks against the alternative of no cointegration (ACK test). In this paper, we systematically examine the ACK test along several dimensions: sample size, kernel selection, bandwidth selection, the maximum value of the first order autocorrelation coefficient allowed in the automated bandwidth estimators proposed by Andrews (1991) and break height. We then compare statistical error frequencies to those of the test proposed by Gregory and Hansen (1996) for the null of no cointegration against the alternative of cointegration with a structural break. We find that the ACK test performs better than the Gregory and Hansen (1996) test in some cases, especially when the data generating process does not contain a cointegration vector. If there is a cointegration vector, the ACK test usually leads to larger statistical error frequencies. The ACK test should hence be used in combination with other tests for cointegration.

Suggested Citation

  • Alexander Ludwig, 2013. "Testing the null of cointegration with a structural break: optimal kernel and bandwidth selection," Economics Bulletin, AccessEcon, vol. 33(4), pages 2828-2839.
  • Handle: RePEc:ebl:ecbull:eb-13-00135
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    File URL: http://www.accessecon.com/Pubs/EB/2013/Volume33/EB-13-V33-I4-P265.pdf
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    References listed on IDEAS

    as
    1. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, vol. 70(1), pages 99-126, January.
    2. Kejriwal, Mohitosh & Perron, Pierre, 2010. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 503-522.
    3. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    4. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-277, August.
    5. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    6. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, vol. 70(1), pages 99-126, January.
    7. Kejriwal Mohitosh, 2008. "Cointegration with Structural Breaks: An Application to the Feldstein-Horioka Puzzle," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-39, March.
    8. Kurozumi, Eiji, 2002. "Testing for stationarity with a break," Journal of Econometrics, Elsevier, vol. 108(1), pages 63-99, May.
    9. Kejriwal, Mohitosh & Perron, Pierre, 2008. "The limit distribution of the estimates in cointegrated regression models with multiple structural changes," Journal of Econometrics, Elsevier, vol. 146(1), pages 59-73, September.
    10. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2006. "Testing the Null of Cointegration with Structural Breaks," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(5), pages 623-646, October.
    11. Juhl, Ted & Xiao, Zhijie, 2009. "Tests for changing mean with monotonic power," Journal of Econometrics, Elsevier, vol. 148(1), pages 14-24, January.
    12. Yoichi Arai & Eiji Kurozumi, 2007. "Testing for the Null Hypothesis of Cointegration with a Structural Break," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 705-739.
    13. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
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    Cited by:

    1. Alexander Ludwig, 2014. "Credit risk-free sovereign bonds under Solvency II: a cointegration analysis with consistently estimated structural breaks," Applied Financial Economics, Taylor & Francis Journals, vol. 24(12), pages 811-823, June.

    More about this item

    Keywords

    cointegration; structural breaks; kernel selection; bandwidth selection; statistical error frequencies;

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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