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

Author

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  • Perron, Pierre
  • Yabu, Tomoyoshi
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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Suggested Citation

  • 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.
    • Handle: RePEc:bes:jnlbes:v:27:i:3:y:2009:p:369-396
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    References listed on IDEAS

    as
    1. 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.
    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.
    3. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    4. 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.
    5. 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.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. 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.
    8. 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(6), pages 818-848, December.
    9. 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.
    10. 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.
    11. 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.
    12. repec:cup:etheor:v:13:y:1997:i:6:p:818-49 is not listed on IDEAS
    13. 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.
    14. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    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. Pierre Perron, 2005. "Dealing with Structural Breaks," Boston University - Department of Economics - Working Papers Series WP2005-017, Boston University - Department of Economics.
    17. 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.
    18. 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.
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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