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A CUSUM test for cointegration using regression residuals

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  • Xiao, Zhijie
  • Phillips, Peter C. B.

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 108 (2002)
Issue (Month): 1 (May)
Pages: 43-61

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Handle: RePEc:eee:econom:v:108:y:2002:i:1:p:43-61

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, Econometric Society, vol. 60(2), pages 271-85, March.
  2. 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.
  3. Hao, K. & Inder, B., 1994. "A Diagnostic Test for Structural Change in Cointegrated Regression Models," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 19/94, Monash University, Department of Econometrics and Business Statistics.
  4. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
  5. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  6. Hansen, Bruce E., 1992. "Efficient estimation and testing of cointegrating vectors in the presence of deterministic trends," Journal of Econometrics, Elsevier, Elsevier, vol. 53(1-3), pages 87-121.
  7. 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.
  8. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, Econometric Society, vol. 58(1), pages 165-93, January.
  9. 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.
  10. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, Econometric Society, vol. 59(5), pages 1329-63, September.
  11. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, Econometric Society, vol. 64(4), pages 763-812, July.
  12. Hansen, Bruce E, 2002. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 45-59, January.
  13. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1551-80, November.
  14. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers, Michigan State - Econometrics and Economic Theory 8905, Michigan State - Econometrics and Economic Theory.
  15. John C. Chao & Peter C.B. Phillips, 1997. "Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure," Cowles Foundation Discussion Papers 1155, Cowles Foundation for Research in Economics, Yale University.
  16. 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.
  17. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  18. 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.
  19. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
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Citations

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Cited by:
  1. Xiao, Zhijie, 2012. "Robust inference in nonstationary time series models," Journal of Econometrics, Elsevier, Elsevier, vol. 169(2), pages 211-223.
  2. Roberto Basile & Mauro Costantini & Sergio Destefanis, 2005. "Unit root and cointegration tests for cross-sectionally correlated panels. Estimating regional production functions," CELPE Discussion Papers 94, CELPE - Centre of Labour Economics and Economic Policy, University of Salerno, Italy.
  3. Gu, Jingping & Liang, Zhongwen, 2014. "Testing cointegration relationship in a semiparametric varying coefficient model," Journal of Econometrics, Elsevier, Elsevier, vol. 178(P1), pages 57-70.
  4. 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.
  5. Taipalus, Katja, 2012. "Detecting asset price bubbles with time-series methods," Scientific Monographs, Bank of Finland E:47/2012, Bank of Finland.
  6. Xiao, Zhijie, 2009. "Quantile cointegrating regression," Journal of Econometrics, Elsevier, Elsevier, vol. 150(2), pages 248-260, June.
  7. 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.
  8. 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.
  9. Singh, Tarlok, 2010. "Does domestic saving cause economic growth? A time-series evidence from India," Journal of Policy Modeling, Elsevier, Elsevier, vol. 32(2), pages 231-253, March.
  10. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, Elsevier, vol. 152(2), pages 81-92, October.
  11. 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.
  12. 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.
  13. 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.
  14. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents, Nobel Prize Committee 2003-1, Nobel Prize Committee.
  15. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 124(1), pages 187-201, January.
  16. 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.

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