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Testing for a unit root in the presence of a possible break in trend

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

Abstract

In this paper we consider the issue of testing a time series for a unit root in the possible presence of a break in a linear deterministic trend at some unknown point in the series. We propose a break fraction estimator which, in the presence of a break in trend, is consistent for the true break fraction at rate Op(T^-1) when there is either a unit root or near-unit root in the stochastic component of the series. In contrast to other estimators available in the literature, when there is no break in trend, our proposed break fraction estimator converges to zero at rate Op(T^-1/2). Used in conjunction with a quasi difference (QD) detrended unit root test that incorporates a trend break regressor in the deterministic component, we show that these rates of convergence ensure that known break fraction null critical values are applicable asymptotically. Unlike available procedures in the literature this holds even if there is no break in trend (the true break fraction is zero), in which case the trend break regressor is dropped from the deterministic component and standard QD detrended unit root test critical values then apply. We also propose a second testing procedure which makes use of a formal pre-test for a trend break in the series, including a trend break regressor only where the pre-test rejects the null of no break. Both procedures ensure that the correctly sized (near-) efficient unit root test that allows (does not allow) for a break in trend is applied in the limit when a trend break does (does not) occur.

Suggested Citation

  • David Harris & David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007. "Testing for a unit root in the presence of a possible break in trend," Discussion Papers 07/04, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:07/04
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    1. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 435-463.
    2. Ozgen Sayginsoy & Tim Vogelsang, 2004. "Powerful Tests of Structural Change That are Robust to Strong Serial Correlation," Discussion Papers 04-08, University at Albany, SUNY, Department of Economics.
    3. Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August.
    4. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    5. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    6. 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.
    7. 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(4), pages 995-1029, August.
    8. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    9. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    10. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-287, July.
    11. Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
    12. 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.
    13. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
    14. Kim, Dukpa & Perron, Pierre, 2009. "Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses," Journal of Econometrics, Elsevier, vol. 148(1), pages 1-13, January.
    15. Perron, Pierre & Yabu, Tomoyoshi, 2009. "Estimating deterministic trends with an integrated or stationary noise component," Journal of Econometrics, Elsevier, vol. 151(1), pages 56-69, July.
    16. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    17. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-364, Oct.-Dec..
    18. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 237-250, July.
    19. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    20. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    21. Cavaliere, Giuseppe & Georgiev, Iliyan, 2007. "Testing For Unit Roots In Autoregressions With Multiple Level Shifts," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1162-1215, December.
    22. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(4), pages 736-749, August.
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