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Testing for unit roots in time series with level shifts

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  • Saikkonen, Pentti
  • Lütkepohl, Helmut

Abstract

Tests for unit roots in univariate time series with level shifts are proposed and investigated. The level shift is assumed to occur at a known time. It may be a simple one-time shift which can be captured by a dummy variable or it may have a more general form which can be modeled by some general nonlinear transition function. There may also be more than one shift point and there may be other deterministic terms such as a linear trend term or seasonal components. It is proposed to estimate the deterministic parts of the series in a first step by a generalized least squares procedure subtract the estimated deterministic terms from the series and apply standard unit root tests to the residuals. It is shown that the tests have known asymptotic distributions under the null hypothesis of a unit root and nearly optimal asymptotic power under local alternatives. The procedure is applied to German macroeconomic time series which have a level shift in 1990 where the reunification took place.

Suggested Citation

  • Saikkonen, Pentti & Lütkepohl, Helmut, 1999. "Testing for unit roots in time series with level shifts," SFB 373 Discussion Papers 1999,27, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:199927
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    References listed on IDEAS

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    1. 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.
    2. 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(02), pages 359-368, February.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. Hwang, Jaeyoun & Schmidt, Peter, 1996. "Alternative methods of detrending and the power of unit root tests," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 227-248.
    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    6. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
    7. Monta s, Antonio & Reyes, Marcelo, 1998. "Effect Of A Shift In The Trend Function On Dickey Fuller Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 14(03), pages 355-363, June.
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    Cited by:

    1. Nicolas Million, 2003. "The Fisher Effect revisited through an efficient non linear unit root testing procedure," Applied Economics Letters, Taylor & Francis Journals, vol. 10(15), pages 951-954.

    More about this item

    Keywords

    unit root; structural shift; autoregression; Univariate time series;

    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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