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

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  • Bent Nielsen

    (Nuffield College, University of Oxford)

Abstract

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

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    1. Saikkonen, Pentti & Lütkepohl, Helmut, 2000. "Testing For The Cointegrating Rank Of A Var Process With An Intercept," Econometric Theory, Cambridge University Press, vol. 16(3), pages 373-406, June.
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    Cited by:

    1. Patrick Marsh, 2019. "Properties of the power envelope for tests against both stationary and explosive alternatives: the effect of trends," Discussion Papers 19/03, University of Nottingham, Granger Centre for Time Series Econometrics.

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    Keywords

    Envelope power function; maximal invariant parameter; maximal invariant statistic; most stringent test; unit root tests.;
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