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Size distortion of bootstrap tests: application to a unit root test

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  • Russell Davidson

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579, CIREG - Centre interuniversitaire de recherche en économie quantitative - Université de Montréal, Department of Economics, McGill University - McGill University)

Abstract

Testing for a unit root in a series obtained by summing a stationary MA(1) process with a parameter close to -1 leads to serious size distortions under the null, on account of the near cancellation of the unit root by the MA component in the driving stationary series. The situation is analysed from the point of view of bootstrap testing, and an exact quantitative account is given of the error in rejection probability of a bootstrap test. A particular method of estimating the MA parameter is recommended, as it leads to very little distortion even when the MA parameter is close to -1. A new bootstrap procedure with still better properties is proposed. While more computationally demanding than the usual bootstrap, it is much less so than the double bootstrap.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00443561.

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Date of creation: 30 Dec 2009
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Handle: RePEc:hal:wpaper:halshs-00443561

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Keywords: Unit root test; bootstrap; MA(1); size distortion;

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