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  • Cited by 8
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Smeekes, Stephan and Taylor, A.M. Robert 2012. BOOTSTRAP UNION TESTS FOR UNIT ROOTS IN THE PRESENCE OF NONSTATIONARY VOLATILITY. Econometric Theory, Vol. 28, Issue. 02, p. 422.

    Marsh, Patrick 2011. SADDLEPOINT AND ESTIMATED SADDLEPOINT APPROXIMATIONS FOR OPTIMAL UNIT ROOT TESTS. Econometric Theory, Vol. 27, Issue. 05, p. 1026.

    Martellosio, Federico 2011. NONTESTABILITY OF EQUAL WEIGHTS SPATIAL DEPENDENCE. Econometric Theory, Vol. 27, Issue. 06, p. 1369.

    Forchini, G. 2009. Some properties of tests for parameters that can be arbitrarily close to being unidentified. Journal of Statistical Planning and Inference, Vol. 139, Issue. 9, p. 3193.

    Harvey, David I. Leybourne, Stephen J. and Taylor, A.M. Robert 2009. UNIT ROOT TESTING IN PRACTICE: DEALING WITH UNCERTAINTY OVER THE TREND AND INITIAL CONDITION. Econometric Theory, Vol. 25, Issue. 03, p. 587.

    Marsh, Patrick 2009. THE PROPERTIES OF KULLBACK–LEIBLER DIVERGENCE FOR THE UNIT ROOT HYPOTHESIS. Econometric Theory, Vol. 25, Issue. 06, p. 1662.

    Marsh, Patrick 2009. COMMENTARIES ON “Unit Root Testing in Practice: Dealing with Uncertainty over the Trend and Initial Condition,” by David I. Harvey, Stephen J. Leybourne, and A.M. Robert Taylor. Econometric Theory, Vol. 25, Issue. 03, p. 637.

    Marsh, Patrick 2008. Conditional Information in Projections of Gaussian Vectors. Communications in Statistics - Theory and Methods, Vol. 38, Issue. 3, p. 332.



  • Patrick Marsh (a1)
  • DOI:
  • Published online: 01 August 2007

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.

Corresponding author
Address correspondence to Patrick Marsh, Department of Economics, University of York, Heslington, York YO10 5DD; e-mail:
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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