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A CUSUM Test for Cointegration Using Regression Residuals

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Abstract

We show that the conventional CUSUM test for structural change can be applied to cointegrating regression residuals leading to a consistent residual based test for the null hypothesis of cointegration. The proposed tests are semiparametric and utilize fully modified residuals to correct for endogeneity and serial correlation and to scale out nuisance parameters. The limit distribution of the test is derived under both the null and the alternative hypothesis. The tests are easy to use and are found to perform quite well in a Monte Carlo experiment.

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  • Zhijie Xiao & Peter C.B. Phillips, 2001. "A CUSUM Test for Cointegration Using Regression Residuals," Cowles Foundation Discussion Papers 1329, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1329
    Note: CFP 1046.
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    1. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
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    5. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    6. Zhijie Xiao, 2001. "Testing the Null Hypothesis of Stationarity Against an Autoregressive Unit Root Alternative," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(1), pages 87-105, January.
    7. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    8. Kang Hao & Inder, Brett, 1996. "Diagnostic test for structural change in cointegrated regression models," Economics Letters, Elsevier, vol. 50(2), pages 179-187, February.
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    10. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    11. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    12. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-285, March.
    13. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 87-121.
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    15. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 45-59, January.
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    17. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    18. Sheather, Simon J., 1986. "An improved data-based algorithm for choosing the window width when estimating the density at a point," Computational Statistics & Data Analysis, Elsevier, vol. 4(1), pages 61-65, June.
    19. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
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    More about this item

    Keywords

    Bandwidth; CUSUM test; Fully modified regression; Null of cointegration; Residual based test; Semiparametric method;
    All these keywords.

    JEL classification:

    • 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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