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

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  • Oleg Glouchakov

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    (Department of Economics, York University)

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    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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    Bibliographic Info

    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
    Date of revision:
    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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    References

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    1. Bai, Jushan, 1999. "Likelihood ratio tests for multiple structural changes," Journal of Econometrics, Elsevier, vol. 91(2), pages 299-323, August.
    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. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477444, April.
    4. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    5. repec:cup:etheor:v:13:y:1997:i:3:p:315-52 is not listed on IDEAS
    6. 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.
    7. David N. DeJong & Hariharan Dharmarajan & Roman Liesenfeld & Jean-Francois Richard, 2005. "On the Structural Stability of U.S. GDP," Working Papers 214, University of Pittsburgh, Department of Economics, revised Jan 2005.
    8. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
    9. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521405515, April.
    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. Wooldridge, Jeffrey M. & White, Halbert, 1988. "Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 4(02), pages 210-230, August.
    12. Bruce E. Hansen, 1995. "Approximate Asymptotic P-Values for Structural Change Tests," Boston College Working Papers in Economics 297., Boston College Department of Economics.
    13. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477451, April.
    14. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    15. Jushan Bai, 1995. "Estimating Multiple Breaks One at a Time," Working papers 95-18, Massachusetts Institute of Technology (MIT), Department of Economics.
    16. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, April.
    17. Jean-Yves Pitarakis, 2003. "Least Squares Estimation and Tests of Breaks in Mean and Variance under Misspecification," Econometrics 0312004, EconWPA.
    18. 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.
    19. Hansen, Bruce E., 1992. "Testing for parameter instability in linear models," Journal of Policy Modeling, Elsevier, vol. 14(4), pages 517-533, August.
    20. Dufour, J.M., 1981. "Recursive Stability Analysis of Linear Regression Relationships," Cahiers de recherche 8129, Universite de Montreal, Departement de sciences economiques.
    21. Kramer, Walter & Ploberger, Werner & Alt, Raimund, 1988. "Testing for Structural Change in Dynamic Models," Econometrica, Econometric Society, vol. 56(6), pages 1355-69, November.
    22. 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.
    23. 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.
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