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Break date estimation for models with deterministic structural change

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  • David I. Harvey
  • Stephen J. Leybourne
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    Abstract

    In this paper we consider estimating the timing of a break in level and/or trend when the order of integration and autocorrelation properties of the data are unknown. For stationary innovations, break point estimation is commonly performed by minimizing the sum of squared residuals across all candidate break points, using a regression of the levels of the series on the assumed deterministic components. For unit root processes, the obvious modification is to use a first differenced version of the regression, while a further alternative in a stationary autoregressive setting is to consider a GLS-type quasi-differenced regression. Given uncertainty over which of these approaches to adopt in practice, we develop a hybrid break fraction estimator that selects from the levels-based estimator, the first-difference-based estimator, and a range of quasi-difference-based estimators, according to which achieves the global minimum sum of squared residuals. We establish the asymptotic properties of the estimators considered, and compare their performance in practically relevant sample sizes using simulation. We find that the new hybrid estimator has desirable asymptotic properties and performs very well in finite samples, providing a reliable approach to break date estimation without requiring decisions to be made regarding the autocorrelation properties of the data.

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    File URL: http://www.nottingham.ac.uk/economics/grangercentre/papers/13-02.pdf
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    Bibliographic Info

    Paper provided by University of Nottingham, Granger Centre for Time Series Econometrics in its series Discussion Papers with number 13/02.

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    Handle: RePEc:not:notgts:13/02

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    Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
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    Web page: http://www.nottingham.ac.uk/economics/grangercentre/
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    Keywords: Break point estimation; Break in level; Break in trend; Local-to-zero breaks.;

    References

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    1. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Testing for Shifts in Trend With an Integrated or Stationary Noise Component," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(3), pages 369-396.
    2. Harris, David & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Testing For A Unit Root In The Presence Of A Possible Break In Trend," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1545-1588, December.
    3. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    4. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
    5. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2010. "Robust methods for detecting multiple level breaks in autocorrelated time series," Journal of Econometrics, Elsevier, vol. 157(2), pages 342-358, August.
    6. Jingjing Yang, 2012. "Break point estimators for a slope shift: levels versus first differences," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 154-169, 02.
    7. James H. Stock & Mark W. Watson, 1994. "Evidence on structural instability in macroeconomic times series relations," Working Paper Series, Macroeconomic Issues 94-13, Federal Reserve Bank of Chicago.
    8. Vogelsang, Timothy J, 1998. "Testing for a Shift in Mean without Having to Estimate Serial-Correlation Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 73-80, January.
    9. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
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