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Testing joint hypotheses when one of the alternatives is one-sided

  • K Abadir
  • W Distaso
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    We propose a class of statistics where the direction of one of the alternatives is incorporated. We modify a class of multivariate tests with elliptical confidence regions, not necessarily arising from normal-based distribution theory. The resulting statistics are easy to compute, they do not require the re-estimation of models subject to one-sided inequality restrictions, and their distributions do not require bounds-based inference. We derive exact explicit distributions, then prove some desirable properties of our class of modified tests. We then illustrate the relevance of the method by applying it to devising an improved test of random walks in autoregressive models with deterministic components. In this example, the usual alternative to a unit root is one-sided in the direction of stable roots, while deterministic components are allowed to go either way, and we show that it is beneficial to take the partially one-sided nature of the alternative into account.

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    Paper provided by Department of Economics, University of York in its series Discussion Papers with number 05/13.

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    Handle: RePEc:yor:yorken:05/13
    Contact details of provider: Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
    Phone: (0)1904 323776
    Fax: (0)1904 323759
    Web page: http://www.york.ac.uk/economics/
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