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Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis

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  • Michael Jansson

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

This paper derives asymptotic power envelopes for tests of the unit root hypothesis in a zero-mean AR(1) model. The power envelopes are derived using the limits of experiments approach and are semiparametric in the sense that the underlying error distribution is treated as an unknown infinitedimensional nuisance parameter. Adaptation is shown to be possible when the error distribution is known to be symmetric and to be impossible when the error distribution is unrestricted. In the latter case, two conceptually distinct approaches to nuisance parameter elimination are employed in the derivation of the semiparametric power bounds. One of these bounds, derived under an invariance restriction, is shown by example to be sharp, while the other, derived under a similarity restriction, is conjectured not to be globally attainable.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2007-12.

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Length: 50
Date of creation: 25 Jun 2007
Date of revision:
Handle: RePEc:aah:create:2007-12

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Web page: http://www.econ.au.dk/afn/

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Keywords: Unit root testing; semiparametric efficiency;

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References

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  1. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation for Research in Economics, Yale University.
  2. Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University.
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Citations

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Cited by:
  1. Hallin, M. & Akker, R. van den & Werker, B.J.M., 2012. "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Discussion Paper 2012-089, Tilburg University, Center for Economic Research.
  2. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2009. "Hypothesis testing in econometrics," IEW - Working Papers 444, Institute for Empirical Research in Economics - University of Zurich.
  3. Marc Hallin & Ramon van den Akker & Bas Werker, 2009. "A class of Simple Semiparametrically Efficient Rank-Based Unit Root Tests," Working Papers ECARES 2009_001, ULB -- Universite Libre de Bruxelles.
  4. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
  5. Michael Jansson & Morten Ørregaard Nielsen, 2012. "Nearly Efficient Likelihood Ratio Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 80(5), pages 2321-2332, 09.
  6. 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.
  7. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2011. "A class of simple distribution-free rank-based unit root tests," Journal of Econometrics, Elsevier, vol. 163(2), pages 200-214, August.
  8. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, 2007. "Unit root testing in practice: dealing with uncertainty over the trend and initial condition," Discussion Papers 07/03, University of Nottingham, Granger Centre for Time Series Econometrics.
  9. Becheri, I.G., 2012. "Limiting experiments for panel-data and jump-diffusion models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-5661649, Tilburg University.
  10. Becheri, I.G. & Drost, F.C. & Akker, R. van den, 2013. "Asymptotically UMP Panel Unit Root Tests," Discussion Paper 2013-017, Tilburg University, Center for Economic Research.

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