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Power of tests for unit roots in the presence of a linear trend


  • Bent Nielsen

    () (Nuffield College, University of Oxford)


Dickey and Fuller (1981) suggested unit root tests for an autoregressive model with a linear trend and a fixed initial value. This model has nuisance parameters so later authors have often worked with a slightly different model with a random initial value in which nuisance parameters can be eliminated by an invariant reduction of the model. This facilitates computation of envelope power functions and comparison of the relative performance of different unit root tests. It is shown here that invariance arguments also can be used when comparing power within the model with fixed initial value. Despite the apparently small difference between the two models the relative performance of unit root tests turns out to be very different.

Suggested Citation

  • Bent Nielsen, 2003. "Power of tests for unit roots in the presence of a linear trend," Economics Papers 2003-W22, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:0322

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    References listed on IDEAS

    1. Saikkonen, Pentti & L tkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(03), pages 373-406, June.
    2. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
    3. Elena Andreou & Aris Spanos, 2003. "Statistical Adequacy and the Testing of Trend Versus Difference Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 217-237, January.
    4. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    5. Doornik, Jurgen A & Hendry, David F & Nielsen, Bent, 1998. " Inference in Cointegrating Models: UK M1 Revisited," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 533-572, December.
    6. Nielsen, Bent & Rahbek, Anders, 2000. " Similarity Issues in Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 5-22, February.
    7. 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.
    8. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 369-384.
    9. Abadir, Karim M. & Distaso, Walter, 2007. "Testing joint hypotheses when one of the alternatives is one-sided," Journal of Econometrics, Elsevier, vol. 140(2), pages 695-718, October.
    10. Doornik, Jurgen A. & O'Brien, R. J., 2002. "Numerically stable cointegration analysis," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 185-193, November.
    11. Francke, Marc K. & de Vos, Aart F., 2007. "Marginal likelihood and unit roots," Journal of Econometrics, Elsevier, vol. 137(2), pages 708-728, April.
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    Envelope power function; maximal invariant parameter; maximal invariant statistic; most stringent test; unit root tests.;

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