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Joint change point estimation in regression coeffcients and variances of the errors of a linear model

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Author Info
Oleg Glouchakov () (Department of Economics, York University)
Abstract

This paper describes how to estimate the alternative model that admits a one-time break in coeffcients of a linear regression function and variances of the errors. Bai and Perron (1998) introduced an estimation and testing procedure for multiple breaks in regression coeffcients. We limit the number of breaks to one but extend the estimation to the alternative model that allows for variances of the errors to break too. The method is based on application of specific objective functions in conjunction with the tests ofstructural change. In particular, sup-Wald test of Andrews (1993) can be used to detect structural breaks. Andrews and Ploberger (1994) introduce optimal tests of constancy of model parameters when the change point is unknown. However, these tests lose their power optimality properties when the break happens in both the mean and the variance of a process. For such an alternative we introduce a statistic with a modified measure of a distance between model parameters before and after the break. In a Monte-Carlo experiment we show that the power of the corresponding sup-test dominates that of the sup-Wald test. If a change point is known, then the test based on this statistic is uniformly more powerful than the Wald test.

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Paper provided by York University, Department of Economics in its series Working Papers with number 2006_3.

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Length: 49 pages
Date of creation: Mar 2006
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Handle: RePEc:yca:wpaper:2006_3

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Related research
Keywords: Change point estimation; asymptotic distribution; Wald statistic; parameter instability; structural change;

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Find related papers by JEL classification:
C0 - Mathematical and Quantitative Methods - - General
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General

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  1. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May. [Downloadable!] (restricted)
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  2. 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. [Downloadable!] (restricted)
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  3. Altissimo, F. & Corradi, V., 2000. "Strong Rules for Detecting the Number of Breaks in a Time Series," Discussion Papers 00/11, University of Exeter, School of Business and Economics.
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  4. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-69, November. [Downloadable!] (restricted)
  5. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(03), pages 315-352, June. [Downloadable!]
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  6. Dufour, J.M., 1981. "Recursive Stability Analysis of Linear Regression Relationships," Cahiers de recherche 8129, Universite de Montreal, Departement de sciences economiques.
  7. 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. [Downloadable!] (restricted)
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  8. Hansen, Bruce E, 1997. "Approximate Asymptotic P Values for Structural-Change Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 60-67, January.
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  9. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July. [Downloadable!] (restricted)
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  10. Jean-Yves Pitarakis, 2004. "Least squares estimation and tests of breaks in mean and variance under misspecification," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 32-54, 06. [Downloadable!] (restricted)
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  11. Hansen, Bruce E., 1992. "Testing for parameter instability in linear models," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 517-533, August. [Downloadable!] (restricted)
  12. Altissimo, Filippo & Corradi, Valentina, 2003. "Strong rules for detecting the number of breaks in a time series," Journal of Econometrics, Elsevier, vol. 117(2), pages 207-244, December. [Downloadable!] (restricted)
  13. repec:cup:etheor:v:13:y:1997:i:3:p:315-52 is not listed on IDEAS
  14. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
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  15. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July. [Downloadable!] (restricted)
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  16. Ploberger, Werner & Kramer, Walter & Kontrus, Karl, 1989. "A new test for structural stability in the linear regression model," Journal of Econometrics, Elsevier, vol. 40(2), pages 307-318, February. [Downloadable!] (restricted)
  17. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August. [Downloadable!] (restricted)
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