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Robust methods for detecting multiple level breaks in autocorrelated time series [Revised to become No. 10/01 above]

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

Abstract

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 standardised 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. An empirical application of the methods proposed in this paper suggests that the majority of the stock price series which comprise the NASDAQ 100 index display level breaks.

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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 09/01.

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Date of creation: Mar 2009
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Handle: RePEc:not:notgts:09/01

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Postal: School of Economics University of Nottingham University Park Nottingham NG7 2RD
Phone: (44) 0115 951 5620
Fax: (0115) 951 4159
Web page: http://www.nottingham.ac.uk/economics/grangercentre/
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Related research

Keywords: Level breaks; unit root; moving means; long run variance estimation; robust tests; breakpoint estimation;

References

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  1. David I. Harvey & Stephen J. Leybourne & A.M. Robert Taylor, . "Simple, Robust and Powerful Tests of the Breaking Trend Hypothesis," Discussion Papers 06/11, University of Nottingham, School of Economics.
  2. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  3. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  4. Bunzel, Helle & Vogelsang, Timothy J., 2003. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation with an Application to the Prebisch-Singer Hypothesis," Staff General Research Papers 10353, Iowa State University, Department of Economics.
  5. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007. "Unit root testing in practice: dealing with uncertainty over the trend and initial condition," Discussion Papers 07/03, University of Nottingham, Granger Centre for Time Series Econometrics.
  6. 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.
  7. Peter Burridge & A. M. Robert Taylor, 2006. "Additive Outlier Detection Via Extreme-Value Theory," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 685-701, 09.
  8. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, 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.
  10. Pierre Perron & Tomoyoshi Yabu, 2005. "Testing for Shifts in Trend with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-026, Boston University - Department of Economics.
  11. 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.
  12. Perron, P. & Rodriguez, G., 2000. "Seraching for Additive Outliers in Nonstationary Time Series," Working Papers 0005e, University of Ottawa, Department of Economics.
  13. Mohitosh Kejriwal & Pierre Perron, 2009. "A Sequential Procedure to Determine the Number of Breaks in Trend with an Integrated or Stationary Noise Component," Purdue University Economics Working Papers 1217, Purdue University, Department of Economics.
  14. 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.
  15. 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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Cited by:
  1. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," PSE Working Papers halshs-00564897, HAL.

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