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Testing for unit roots in time series with level shifts

  • Saikkonen, Pentti
  • Lütkepohl, Helmut

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.

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Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1999,27.

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Date of creation: 1999
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Handle: RePEc:zbw:sfb373:199927
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  1. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. 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.
  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(02), pages 359-368, February.
  5. 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.
  6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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