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Testing for Breaks Using Alternating Observations

Author

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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.

Suggested Citation

  • Bunzel, Helle & Iglesias, Emma M., 2006. "Testing for Breaks Using Alternating Observations," Staff General Research Papers Archive 12694, Iowa State University, Department of Economics.
  • Handle: RePEc:isu:genres:12694
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    File URL: http://www2.econ.iastate.edu/papers/p3858-2006-11-09.pdf
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    References listed on IDEAS

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    1. 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.
    2. Donald W. K. Andrews, 2004. "the Block-Block Bootstrap: Improved Asymptotic Refinements," Econometrica, Econometric Society, vol. 72(3), pages 673-700, May.
    3. 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.
    4. 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.
    5. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    6. 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 815-843, August.
    7. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    8. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    9. 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.
    10. 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.
    11. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    12. 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.
    13. 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.
    14. 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.
    15. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    16. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    17. Gibbons, Michael R., 1982. "Multivariate tests of financial models : A new approach," Journal of Financial Economics, Elsevier, vol. 10(1), pages 3-27, March.
    18. 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.
    19. Jushan Bai & Robin L. Lumsdaine & James H. Stock, 1998. "Testing For and Dating Common Breaks in Multivariate Time Series," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 395-432.
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    Cited by:

    1. Attfield, Cliff & Temple, Jonathan R.W., 2010. "Balanced growth and the great ratios: New evidence for the US and UK," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 937-956, December.

    More about this item

    Keywords

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

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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