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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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File URL: http://cowles.econ.yale.edu/P/cd/d13a/d1329.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1329.

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Length: 21 pages
Date of creation: Sep 2001
Date of revision:
Publication status: Published in Journal of Econometrics (2002), 108: 43-61
Handle: RePEc:cwl:cwldpp:1329

Note: CFP 1046.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Bandwidth; CUSUM test; Fully modified regression; Null of cointegration; Residual based test; Semiparametric method;

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References

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  1. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  2. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
  3. 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.
  4. 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.
  5. 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.
  6. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  8. 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.
  9. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-78, September.
  10. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
  11. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  12. Peter C.B. Phillips & Sam Ouliaris, 1987. "Asymptotic Properties of Residual Based Tests for Cointegration," Cowles Foundation Discussion Papers 847R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1988.
  13. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(01), pages 91-115, March.
  14. Kang Hao & Inder, Brett, 1996. "Diagnostic test for structural change in cointegrated regression models," Economics Letters, Elsevier, vol. 50(2), pages 179-187, February.
  15. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-85, March.
  16. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  17. Chao, John C. & Phillips, Peter C. B., 1999. "Model selection in partially nonstationary vector autoregressive processes with reduced rank structure," Journal of Econometrics, Elsevier, vol. 91(2), pages 227-271, August.
  18. Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 205-230.
  19. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
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Citations

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Cited by:
  1. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents 2003-1, Nobel Prize Committee.
  2. Taipalus, Katja, 2012. "Detecting asset price bubbles with time-series methods," Scientific Monographs E:47/2012, Bank of Finland.
  3. Singh, Tarlok, 2010. "Does domestic saving cause economic growth? A time-series evidence from India," Journal of Policy Modeling, Elsevier, vol. 32(2), pages 231-253, March.
  4. Seung Hyun Hong & Peter C. B. Phillips, 2005. "Testing Linearity in Cointegrating Relations with an Application to Purchasing Power Parity," Cowles Foundation Discussion Papers 1541, Cowles Foundation for Research in Economics, Yale University.
  5. Roberto Basile & Mauro Costantini & Sergio Destefanis, 2005. "Unit root and cointegration tests for cross-sectionally correlated panels. Estimating regional production functions," ISAE Working Papers 53, ISTAT - Italian National Institute of Statistics - (Rome, ITALY).
  6. Boutabba, Mohamed Amine & Beaumais, Olivier & Lardic, Sandrine, 2012. "Permit price dynamics in the U.S. SO2 trading program: A cointegration approach," Energy Economics, Elsevier, vol. 34(3), pages 714-722.
  7. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
  8. Kirman, Alan & Teyssiere, Gilles, 2005. "Testing for bubbles and change-points," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 765-799, April.
  9. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, vol. 124(1), pages 187-201, January.
  10. Singh, Tarlok, 2008. "Testing the Saving-Investment correlations in India: An evidence from single-equation and system estimators," Economic Modelling, Elsevier, vol. 25(5), pages 1064-1079, September.
  11. Gu, Jingping & Liang, Zhongwen, 2014. "Testing cointegration relationship in a semiparametric varying coefficient model," Journal of Econometrics, Elsevier, vol. 178(P1), pages 57-70.
  12. Xiao, Zhijie, 2012. "Robust inference in nonstationary time series models," Journal of Econometrics, Elsevier, vol. 169(2), pages 211-223.
  13. Zhijie Xiao, 2009. "Quantile Cointegrating Regression," Boston College Working Papers in Economics 708, Boston College Department of Economics.
  14. Chan, Hing Lin & Woo, Kai-Yin, 2008. "Testing for stochastic explosive root bubbles in Asian emerging stock markets," Economics Letters, Elsevier, vol. 99(1), pages 185-188, April.
  15. Noureddine Benlagha, 2013. "The Long-run Relationship among Index-linked Bonds and Conventional Bonds," Review of Economics & Finance, Better Advances Press, Canada, vol. 3, pages 15-24, February.
  16. Caporale, Guglielmo Maria & Pittis, Nikitas, 2004. "Robustness of the CUSUM and CUSUM-of-Squares Tests to Serial Correlation, Endogeneity and Lack of Structural Invariance. Some Monte Carlo Evidence," Economics Series 157, Institute for Advanced Studies.

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