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The available information for invariant tests of a unit root

Marsh, P.W. (2007) The available information for invariant tests of a unit root. Econometric Theory, 23 (4). pp. 686-710. ISSN 0266-4666

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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.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Economics and Related Studies (York)
Depositing User: York RAE Import
Date Deposited: 11 Jun 2009 15:42
Last Modified: 11 Jun 2009 15:42
Published Version: http://dx.doi.org/10.1017/S0266466607070296
Status: Published
Publisher: Cambridge University Press
Identification Number: 10.1017/S0266466607070296
URI: http://eprints.whiterose.ac.uk/id/eprint/6037

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