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Multiple Change-Point Detection in Linear Regression Models via U-Statistic Type Processes

  • Burcu Kapar
  • William Pouliot

Many procedures have been developed that are suited to testing for multiple changes in parameters of regression models which occur at unknown times. Most notably, Brown, Durbin and Evans [11] and Dufour [15], have developed or extended existing techniques, but said extensions lack power for detecting changes (cf. Kramer, Ploberger, Alt [24] and Pouliot [32] in the intercept parameter of linear regression models. Orasch [26] has developed a stochastic process that easily accommodates testing for many change-points that occur at unknown times. A slight modification of his process is suggested here which improves the power of statistics fashioned from it. These statistics are then used to construct tests to detect multiple changes in intercept in linear regression models. It is also shown here that this slightly altered process, when weighted by appropriately chosen functions, is sensitive to detection of multiple changes in intercept that occur both early and later on in the sample, while maintaining sensitivity to changes that occur in the middle of the sample.

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Paper provided by Department of Economics, University of Birmingham in its series Discussion Papers with number 13-13.

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Length: 34 pages
Date of creation: May 2013
Date of revision:
Handle: RePEc:bir:birmec:13-13
Contact details of provider: Postal: Edgbaston, Birmingham, B15 2TT
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  1. 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.
  2. 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.
  3. Hansen, Bruce E., 1992. "Testing for parameter instability in linear models," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 517-533, August.
  4. 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.
  5. Filippo Altissimo & Valentina Corradi, 2000. "Strong Rules for Detecting the Number of Breaks in a Time Series," Econometric Society World Congress 2000 Contributed Papers 0574, Econometric Society.
  6. Donald W. K. Andrews, 2003. "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum," Econometrica, Econometric Society, vol. 71(1), pages 395-397, January.
  7. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Universite de Montreal, Departement de sciences economiques.
  8. 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.
  9. Ploberger, Werner & Krämer;, Walter, 1990. "The Local Power of the CUSUM and CUSUM of Squares Tests," Econometric Theory, Cambridge University Press, vol. 6(03), pages 335-347, September.
  10. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-69, November.
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