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Spurious Cointegration: The Engle-Granger Test in the Presence of Structural Breaks

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  • Noriega Antonio E.
  • Ventosa-Santaulària Daniel

Abstract

This paper analyses the asymptotic behavior of the Engle-Granger t-test for cointegration when the data include structural breaks, instead of being pure I(1) processes. We find that the test does not possess a limiting distribution, but diverges as the sample size tends to infinity. Calculations involving the asymptotic expression of the t-test , as well as Monte Carlo simulations, reveal that the test can diverge in either direction, making it unreliable as a test for cointegration, when there are neglected breaks in the trend function of the data. Using real data on car sales and murders in the US, we present an empirical illustration of the theoretical results.

Suggested Citation

  • Noriega Antonio E. & Ventosa-Santaulària Daniel, 2006. "Spurious Cointegration: The Engle-Granger Test in the Presence of Structural Breaks," Working Papers 2006-12, Banco de México.
    • Handle: RePEc:bdm:wpaper:2006-12
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    References listed on IDEAS

    as
    1. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    2. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2006. "Spurious Regression Under Broken‐Trend Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 671-684, September.
    3. Kellard, Neil, 2006. "On the robustness of cointegration tests when assessing market efficiency," Finance Research Letters, Elsevier, vol. 3(1), pages 57-64, March.
    4. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    5. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
    6. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    7. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
    8. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    9. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    10. Stephen Leybourne & Paul Newbold, 2003. "Spurious rejections by cointegration tests induced by structural breaks," Applied Economics, Taylor & Francis Journals, vol. 35(9), pages 1117-1121.
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    Cited by:

    1. D. Ventosa-Santaulària, 2009. "Spurious Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-27, August.
    2. Muhammad Akmal & Muhammad Saleem, 2008. "Technical Efficiency of the Banking Sector in Pakistan," SBP Research Bulletin, State Bank of Pakistan, Research Department, vol. 4, pages 61-80.
    3. Víctor-Hugo Alcalá Ríos & Manuel Gómez Zaldívar & Daniel Ventosa-Santaulà ria, 2011. "Paradoja Feldstein-Horioka: el caso de México (1950-2007)," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 26(2), pages 293-313.
    4. Filiz OZKAN, & Ömer OZKAN, & Huseyin Serdar KUYUK, 2012. "Energy Production And Economic Growth: Empirical Evidence From Turkey," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 12(2).
    5. Ozkan, F, 2011. "Steel Industry and The Sector’s Impact On Economical Growth In Turkey," Regional and Sectoral Economic Studies, Euro-American Association of Economic Development, vol. 11(2).

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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