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Robust methods for detecting multiple level breaks in autocorrelated time series

  • Harvey, David I.
  • Leybourne, Stephen J.
  • Taylor, A.M. Robert

In this paper we propose tests for the null hypothesis that a time series process displays a constant level against the alternative that it displays (possibly) multiple changes in level. Our proposed tests are based on functions of appropriately standardized sequences of the differences between sub-sample mean estimates from the series under investigation. The tests we propose differ notably from extant tests for level breaks in the literature in that they are designed to be robust as to whether the process admits an autoregressive unit root (the data are I(1)) or stable autoregressive roots (the data are I(0)). We derive the asymptotic null distributions of our proposed tests, along with representations for their asymptotic local power functions against Pitman drift alternatives under both I(0) and I(1) environments. Associated estimators of the level break fractions are also discussed. We initially outline our procedure through the case of non-trending series, but our analysis is subsequently extended to allow for series which display an underlying linear trend, in addition to possible level breaks. Monte Carlo simulation results are presented which suggest that the proposed tests perform well in small samples, showing good size control under the null, regardless of the order of integration of the data, and displaying very decent power when level breaks occur.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 157 (2010)
Issue (Month): 2 (August)
Pages: 342-358

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Handle: RePEc:eee:econom:v:157:y:2010:i:2:p:342-358
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  3. Pierre Perron & Tomoyoshi Yabu, 2007. "Testing for Shifts in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2007-025, Boston University - Department of Economics.
  4. Leisch, Friedrich & Hornik, Kurt & Kuan, Chung-Ming, 2000. "Monitoring Structural Changes With The Generalized Fluctuation Test," Econometric Theory, Cambridge University Press, vol. 16(06), pages 835-854, December.
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  8. Pierre Perron & Tomoyoshi Yabu, . "Estimating Deterministic Trends with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2006-012, Boston University - Department of Economics, revised Feb 2006.
  9. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  10. Mohitosh Kejriwal & Pierre Perron, 2010. "A sequential procedure to determine the number of breaks in trend with an integrated or stationary noise component," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 305-328, 09.
  11. Sayginsoy, Özgen & Vogelsang, Timothy J., 2011. "Testing For A Shift In Trend At An Unknown Date: A Fixed-B Analysis Of Heteroskedasticity Autocorrelation Robust Ols-Based Tests," Econometric Theory, Cambridge University Press, vol. 27(05), pages 992-1025, October.
  12. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
  13. Perron, Pierre & Vogelsang, Timothy J, 1992. "Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 467-70, October.
  14. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(03), pages 587-636, June.
  15. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  16. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Simple, Robust, And Powerful Tests Of The Breaking Trend Hypothesis," Econometric Theory, Cambridge University Press, vol. 25(04), pages 995-1029, August.
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