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Testing for Breaks Using Alternating Observations

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  • Bunzel, Helle
  • Iglesias, Emma M.

Abstract

This paper proposes several new tests for structural change in the multivariate linear regression model. One of the most popular alternatives are Sup-Wald type tests along the lines of Bai, Lumsdaine and Stock (1998), which Bernard,Idoudi, Khalaf and Yélou (2007) show to have very large size distortions, especially for high dimensional systems. They propose the use of Monte Carlo type tests to control for size in finite samples. In this paper we propose several procedures that find a balance between the two previous approaches. We first estimate the break point using alternating observations, and then use the estimated breakpoint to create a test statistic either with the whole sample or with the observations not used for the breakpoint estimation. For the latter approach, it is then possible to use Monte Carlo methods to control size. In contrast to the Sup-Wald type tests, which have non-standard asymptotic distributions, we show that our tests are asymptotically distributed Chisquare using methods similar to those in Andrews (2004). Additionally, our tests stay asymptotically valid even when the distributional assumption made for the Monte Carlo adjustments is incorrect. We illustrate the new test statistics in the univariate context of discount rates and changes in the interest rates, and also in the multivariate setting of the Capital Asset Pricing Model.

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Bibliographic Info

Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 12694.

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Date of creation: 09 Nov 2006
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Handle: RePEc:isu:genres:12694

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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
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Web page: http://www.econ.iastate.edu
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Related research

Keywords: structural stability; structural change; multivariage linear regression model; breaks; Monte Carlo test; CAPM; discount rate;

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References

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  1. 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.
  2. DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 2005-03, Universite de Montreal, Departement de sciences economiques.
  3. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March.
  6. 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.
  7. Michael J. Dueker, 1992. "The response of market interest rates to discount rate changes," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 78-91.
  8. James H. Stock & Mark W. Watson, 1994. "Evidence on Structural Instability in Macroeconomic Time Series Relations," NBER Technical Working Papers 0164, National Bureau of Economic Research, Inc.
  9. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-43, August.
  10. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  11. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  12. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
  13. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
  14. Bernard, Jean-Thomas & Idoudi, Nadhem & Khalaf, Lynda & Yelou, Clement, 2007. "Finite sample multivariate structural change tests with application to energy demand models," Journal of Econometrics, Elsevier, vol. 141(2), pages 1219-1244, December.
  15. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
  16. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Simulation based finite and large sample tests in multivariate regressions," Journal of Econometrics, Elsevier, vol. 111(2), pages 303-322, December.
  17. Donald W. K. Andrews, 2004. "the Block-Block Bootstrap: Improved Asymptotic Refinements," Econometrica, Econometric Society, vol. 72(3), pages 673-700, 05.
  18. Hansen, Bruce E, 1992. "Tests for Parameter Instability in Regressions with I(1) Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 321-35, July.
  19. Bai, Jushan & Lumsdaine, Robin L & Stock, James H, 1998. "Testing for and Dating Common Breaks in Multivariate Time Series," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 395-432, July.
  20. Ho-Chuan Huang & Wan-hsiu Cheng, 2005. "Tests of the CAPM under structural changes," International Economic Journal, Taylor & Francis Journals, vol. 19(4), pages 523-541.
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