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Efficient estimation and inference in cointegrating regressions with structural change

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  • Eiji Kurozumi
  • Yoichi Arai

Abstract

. This paper investigates an efficient estimation method for a cointegrating regression model with structural change. Our proposal is that we first estimate the break point by minimizing the sum of squared residuals and then, by replacing the break fraction with the estimated one, we estimate the regression model by the canonical cointegrating regression (CCR) method proposed by Park [Econometrica (1992) Vol. 60, pp. 119–143]. We show that the estimator of the break fraction has the same convergence rate as obtained in Bai, Lumsdaine and Stock [Review of Economic Studies (1998) Vol. 65, pp. 395–432] and that the CCR estimator with the estimated break fraction has the same asymptotic property as the estimator with the known break point. However, we also show that our method breaks down when the magnitude of structural change is very small. Simulation experiments reveal how the finite sample distribution approaches the limiting distribution as the magnitude of the break and or the sample size increases.

Suggested Citation

  • Eiji Kurozumi & Yoichi Arai, 2007. "Efficient estimation and inference in cointegrating regressions with structural change," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 545-575, July.
  • Handle: RePEc:bla:jtsera:v:28:y:2007:i:4:p:545-575
    DOI: 10.1111/j.1467-9892.2006.00524.x
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    1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
    2. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    3. Saikkonen, Pentti & Lutkepohl, Helmut, 2000. "Testing for the Cointegrating Rank of a VAR Process with Structural Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 451-464, October.
    4. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    5. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 114(2), pages 261-295, June.
    6. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    7. 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.
    8. Saikkonen, Pentti & Lütkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(3), pages 373-406, June.
    9. Hao, K., 1996. "Testing for Structural Change in Cointegrated Regression Models: Some Comparisons and Generalizations," Monash Econometrics and Business Statistics Working Papers 3/96, Monash University, Department of Econometrics and Business Statistics.
    10. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    11. Gregory, Allan W. & Hansen, Bruce E., 1996. "Residual-based tests for cointegration in models with regime shifts," Journal of Econometrics, Elsevier, vol. 70(1), pages 99-126, January.
    12. Helmut Lütkepohl & Pentti Saikkonen & Carsten Trenkler, 2004. "Testing for the Cointegrating Rank of a VAR Process with Level Shift at Unknown Time," Econometrica, Econometric Society, vol. 72(2), pages 647-662, March.
    13. Lutkepohl, Helmut & Saikkonen, Pentti & Trenkler, Carsten, 2003. "Comparison of tests for the cointegrating rank of a VAR process with a structural shift," Journal of Econometrics, Elsevier, vol. 113(2), pages 201-229, April.
    14. 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.
    15. Quintos, Carmela E, 1995. "Sustainability of the Deficit Process with Structural Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(4), pages 409-417, October.
    16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    17. Lutkepohl, Helmut & Saikkonen, Pentti, 2000. "Testing for the cointegrating rank of a VAR process with a time trend," Journal of Econometrics, Elsevier, vol. 95(1), pages 177-198, March.
    18. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    19. Kang Hao & Inder, Brett, 1996. "Diagnostic test for structural change in cointegrated regression models," Economics Letters, Elsevier, vol. 50(2), pages 179-187, February.
    20. Campos, Julia & Ericsson, Neil R. & Hendry, David F., 1996. "Cointegration tests in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 70(1), pages 187-220, January.
    21. Andrews, Donald W. K. & Lee, Inpyo & Ploberger, Werner, 1996. "Optimal changepoint tests for normal linear regression," Journal of Econometrics, Elsevier, vol. 70(1), pages 9-38, January.
    22. Henrik Hansen & Søren Johansen, 1999. "Some tests for parameter constancy in cointegrated VAR-models," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 306-333.
    23. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    24. Quintos, Carmela E & Phillips, Peter C B, 1993. "Parameter Constancy in Cointegrating Regressions," Empirical Economics, Springer, vol. 18(4), pages 675-706.
    25. 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.
    26. Gregory, Allan W. & Nason, James M. & Watt, David G., 1996. "Testing for structural breaks in cointegrated relationships," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 321-341.
    27. 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.
    28. 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(1), pages 91-115, March.
    29. Gregory, Allan W & Hansen, Bruce E, 1996. "Tests for Cointegration in Models with Regime and Trend Shifts," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 555-560, August.
    30. Seo, Byeongseon, 1998. "Tests For Structural Change In Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 14(2), pages 222-259, April.
    31. Inoue, Atsushi, 1999. "Tests of cointegrating rank with a trend-break," Journal of Econometrics, Elsevier, vol. 90(2), pages 215-237, June.
    32. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(1), pages 1-21, March.
    33. Quintos, Carmela E., 1998. "Stability tests in error correction models," Journal of Econometrics, Elsevier, vol. 82(2), pages 289-315, February.
    34. 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.
    35. Jushan Bai & Robin L. Lumsdaine & James H. Stock, 1998. "Testing For and Dating Common Breaks in Multivariate Time Series," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 395-432.
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    Cited by:

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    2. Yoichi Arai & Eiji Kurozumi, 2007. "Testing for the Null Hypothesis of Cointegration with a Structural Break," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 705-739.
    3. 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.
    4. Yoichi Arai & Eiji Kurozumi, 2005. "Testing for the Null Hypothesis of Cointegration with Structural Breaks (Subsequently published in "Econometric Reviews", Volume 26, Issue 6 November 2007, pages 705 - 739. )," CARF F-Series CARF-F-022, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Mariam Camarero & Josep Lluís Carrion-i-Silvestre & Cecilio Tamarit, 2021. "Análisis de la sostenibilidad del sector exterior en la OCDE con técnicas de multicointegración," Working Papers 2112, Department of Applied Economics II, Universidad de Valencia.

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