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The Available Information For Invariant Tests Of A Unit Root

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  • Marsh, Patrick

Abstract

This paper considers the information available to invariant unit root tests at and near the unit root. Because all invariant tests will be functions of the maximal invariant, the Fisher information in this statistic will be the available information. The main finding of the paper is that the available information for all tests invariant to a linear trend is zero at the unit root. This result applies for any sample size, over a variety of distributions and correlation structures, and is robust to the inclusion of any other deterministic component. In addition, an explicit upper bound upon the power of all invariant unit root tests is shown to depend solely upon the information. This bound is illustrated via a brief simulation study that also examines the impact that different invariance requirements have on power.Thanks are due to Francesco Bravo, Giovanni Forchini, Les Godfrey, Robert Taylor, participants at seminars at the Universities of Birmingham and York and at the ESRC Econometric study group conference, Bristol, 2004, and also to Bruce Hansen, Joel Horowitz, and five anonymous referees. Revisions of this paper have greatly benefited from comments and suggestions from Grant Hillier and Peter Phillips.

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  • Marsh, Patrick, 2007. "The Available Information For Invariant Tests Of A Unit Root," Econometric Theory, Cambridge University Press, vol. 23(4), pages 686-710, August.
    • Handle: RePEc:cup:etheor:v:23:y:2007:i:04:p:686-710_07
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    2. 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.
    3. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(3), pages 587-636, June.
    4. Patrick Marsh, 2019. "The role of information in nonstationary regression," Discussion Papers 19/04, University of Nottingham, Granger Centre for Time Series Econometrics.
    5. Patrick Marsh, "undated". "Saddlepoint Approximations for Optimal Unit Root Tests," Discussion Papers 09/31, Department of Economics, University of York.
    6. Ghoshray, Atanu, 2022. "Trends and persistence of farm-gate coffee prices around the world," 96th Annual Conference, April 4-6, 2022, K U Leuven, Belgium 321166, Agricultural Economics Society - AES.
    7. David I. Harvey, & Stephen J. Leybourne, & A. M. Robert Taylor, 2007. "Testing for a unit root when uncertain about the trend [Revised to become 07/03 above]," Discussion Papers 06/03, University of Nottingham, Granger Centre for Time Series Econometrics.

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