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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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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Find related papers by JEL classification:
  • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

References listed on IDEAS
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  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  2. 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.
  3. 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.
  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. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  6. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "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?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  7. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  8. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  9. Hao, K. & Inder, B., 1994. "A Diagnostic Test for Structural Change in Cointegrated Regression Models," Monash Econometrics and Business Statistics Working Papers 19/94, Monash University, Department of Econometrics and Business Statistics.
  10. 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.
  11. 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.
  12. 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.
  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. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
  15. 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.
  16. 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.
  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. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-85, March.
  19. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
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Cited by:

  1. 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.
  2. Neto, David, 2014. "The FMLS-based CUSUM statistic for testing the null of smooth time-varying cointegration in the presence of a structural break," Economics Letters, Elsevier, vol. 125(2), pages 208-211.
  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. Xiao, Zhijie, 2012. "Robust inference in nonstationary time series models," Journal of Econometrics, Elsevier, vol. 169(2), pages 211-223.
  5. 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.
  6. Taipalus, Katja, 2012. "Detecting asset price bubbles with time-series methods," Scientific Monographs, Bank of Finland, number 2012_047, 06.
  7. 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.
  8. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents 2003-1, Nobel Prize Committee.
  9. 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.
  10. 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.
  11. Zhijie Xiao, 2009. "Quantile Cointegrating Regression," Boston College Working Papers in Economics 708, Boston College Department of Economics.
  12. Xiao, Zhijie, 2009. "Functional-coefficient cointegration models," Journal of Econometrics, Elsevier, vol. 152(2), pages 81-92, October.
  13. Gu, Jingping & Liang, Zhongwen, 2014. "Testing cointegration relationship in a semiparametric varying coefficient model," Journal of Econometrics, Elsevier, vol. 178(P1), pages 57-70.
  14. 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).
  15. repec:hhs:bofism:2012_047 is not listed on IDEAS
  16. David Neto, 2015. "Testing for and dating structural break in smooth time-varying cointegration parameters, with an application to retail gasoline price and crude oil price long-run relationship," Empirical Economics, Springer, vol. 49(3), pages 909-928, November.
  17. Jansson, Michael, 2005. "Point optimal tests of the null hypothesis of cointegration," Journal of Econometrics, Elsevier, vol. 124(1), pages 187-201, January.
  18. 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.
  19. 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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