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Test Procedures for Unit Roots in Time Series with Level Shifts at Unknown Time

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  • Markku Lanne
  • Helmut Lütkepohl
  • Pentti Saikkonen

Abstract

Two types of unit root tests which accommodate a structural level shift at a known point in time are extended to the situation where the break date is unknown. It is shown that for any estimator for the break date the tests have the same asymptotic distribution as the corresponding tests under the known break date assumption. Different estimators of the break date are compared in a Monte Carlo experiment and a recommendation for choosing the break date in small samples is given. Example series from the Nelson–Plosser data set are used to illustrate the performance of our tests.

Suggested Citation

  • Markku Lanne & Helmut Lütkepohl & Pentti Saikkonen, 2003. "Test Procedures for Unit Roots in Time Series with Level Shifts at Unknown Time," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(1), pages 91-115, February.
    • Handle: RePEc:bla:obuest:v:65:y:2003:i:1:p:91-115
    DOI: 10.1111/1468-0084.00036
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    1. Markku Lanne & Helmut Lütkepohl & Pentti Saikkonen, 2003. "Test Procedures for Unit Roots in Time Series with Level Shifts at Unknown Time," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(1), pages 91-115, February.
    2. Lanne, Markku & Lutkepohl, Helmut, 2002. "Unit root tests for time series with level shifts: a comparison of different proposals," Economics Letters, Elsevier, vol. 75(1), pages 109-114, March.
    3. Saikkonen, Pentti & Lütkepohl, Helmut, 2002. "Testing For A Unit Root In A Time Series With A Level Shift At Unknown Time," Econometric Theory, Cambridge University Press, vol. 18(2), pages 313-348, April.
    4. Amsler, Christine & Lee, Junsoo, 1995. "An LM Test for a Unit Root in the Presence of a Structural Change," Econometric Theory, Cambridge University Press, vol. 11(2), pages 359-368, February.
    5. Hsiao,Cheng & Morimune,Kimio & Powell,James L. (ed.), 2001. "Nonlinear Statistical Modeling," Cambridge Books, Cambridge University Press, number 9780521662468, October.
    6. 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.
    7. 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.
    8. Leybourne, Stephen J. & C. Mills, Terence & Newbold, Paul, 1998. "Spurious rejections by Dickey-Fuller tests in the presence of a break under the null," Journal of Econometrics, Elsevier, vol. 87(1), pages 191-203, August.
    9. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-320, July.
    10. Markku Lanne & Helmut Lütkepohl & Pentti Saikkonen, 2002. "Comparison of unit root tests for time series with level shifts," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(6), pages 667-685, November.
    11. 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.
    12. Evans, George W, 1989. "Output and Unemployment Dynamics in the United States: 1950-1985," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(3), pages 213-237, July-Sept.
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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
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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