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Testing for Shifts in Trend with an Integrated or Stationary Noise Component

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Author Info
Pierre Perron () (Department of Economics, Boston University)
Tomoyoshi Yabu () (Department of Economics, Boston University)

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Abstract

This paper considers the problem of testing for structural changes in the trend function of a univariate time series without any prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. We propose a new approach that builds on the work of Perron and Yabu (2005), based on a Feasible Quasi Generalized Least Squares procedure that uses a superefficient estimate of the sum of autoregressive parameters á when á = 1. In the case of a known break date, the resulting Wald test has a chi- square limit distribution in both the I(0) and I(1) cases. When the break date is unknown, the Exp function of Andrews and Ploberger (1994) yields a test with identical limit distributions in the two cases so that a testing procedure with nearly the same size in the I(0) and I(1) cases can be obtained. To improve the finite sample properties of the tests, we used the bias corrected version of the OLS estimate of á proposed by Roy and Fuller (2001). We show our procedure to be substantially more powerful then currently available alternatives and also to have a power function that is close to that attainable if we knew the true value of á in many cases. The extension to the case of multiple breaks is also discussed.

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Publisher Info
Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2007-025.

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Length: 57pages
Date of creation: Mar 2007
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Handle: RePEc:bos:wpaper:wp2007-025

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Related research
Keywords: structural change; unit root; median-unbiased estimates; GLS procedure; super efficient estimates.;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Timothy J. Vogelsang, 1999. "Testing for a Shift in Trend when Serial Correlation is of Unknown Form," Tinbergen Institute Discussion Papers 99-016/4, Tinbergen Institute.
  2. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November. [Downloadable!] (restricted)
    Other versions:
  3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  4. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May. [Downloadable!] (restricted)
  5. Tatsuma Wada & Pierre Perron, 2005. "Trend and Cycles: A New Approach and Explanations of Some Old Puzzles," Computing in Economics and Finance 2005 252, Society for Computational Economics. [Downloadable!]
  6. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
    Other versions:
  7. Ben-David, D. & Papell, D.H., 1995. "The Great War, The Great Crash and Steady State Growth: Some New Evidence an Old Stylized Fact," Papers 36-95, Tel Aviv - the Sackler Institute of Economic Studies.
  8. Kormendi, Roger C & Meguire, Philip, 1990. "A Multicountry Characterization of the Nonstationarity of Aggregate Output," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 22(1), pages 77-93, February. [Downloadable!] (restricted)
  9. repec:cup:etheor:v:13:y:1997:i:6:p:818-49 is not listed on IDEAS
  10. Pierre Perron & Tomoyoshi Yabu, 2005. "Estimating Deterministric Trends with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2005-037, Boston University - Department of Economics. [Downloadable!]
    Other versions:
  11. Vogelsang, Timothy J., 1997. "Wald-Type Tests for Detecting Breaks in the Trend Function of a Dynamic Time Series," Econometric Theory, Cambridge University Press, vol. 13(06), pages 818-848, December. [Downloadable!]
  12. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  13. Pierre Perron, 2005. "Dealing with Structural Breaks," Boston University - Department of Economics - Working Papers Series WP2005-017, Boston University - Department of Economics. [Downloadable!]
  14. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22. [Downloadable!]
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  15. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119. [Downloadable!] (restricted)
  16. Ben-David, Dan & Papell, David H., 1995. "The great wars, the great crash, and steady state growth: Some new evidence about an old stylized fact," Journal of Monetary Economics, Elsevier, vol. 36(3), pages 453-475, December. [Downloadable!] (restricted)
  17. Anindya Roy & Barry Falk & Wayne A. Fuller, 2004. "Testing for Trend in the Presence of Autoregressive Error," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1082-1091, December. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Tatsuma Wada & Pierre Perron, 2005. "An Alternative Trend-Cycle Decomposition using a State Space Model with Mixtures of Normals: Specifications and Applications to International Data," Boston University - Department of Economics - Working Papers Series WP2005-44, Boston University - Department of Economics. [Downloadable!]
    Other versions:
  2. Tatsuma Wada & Pierre Perron, 2006. "State Space Model with Mixtures of Normals: Specifications and Applications to International Data," Boston University - Department of Economics - Working Papers Series WP2006-029, Boston University - Department of Economics. [Downloadable!]
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