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Optimal Fractional Dickey-Fuller Tests for Unit Roots

  • Ignacio N. Lobato

    ()

    (Centro de Investigacion Economica (CIE), Instituto Tecnologico Autonomo de Mexico (ITAM))

  • Carlos Velasco

    ()

    (Departamento de Econometria y Estadistica, Universidad Carlos III de Madrid)

This article studies the fractional Dickey- Fuller (FDF) test for unit roots recently introduced by Dolado, Gonzalo and Mayoral (2002). Apart from the analogy with the Dickey-Fuller test, the main motivation for their method relies on simulations since these authors do not provide any justification for their particular implementation of the FDF test. In order to give additional rationale to the test, we frame the FDF test in a model where a nuisance or auxiliary parameter is not identified under the null hypothesis. Within this framework we investigate optimality aspects of the class of tests indexed by this auxiliary parameter and show that the test proposed by these authors is not optimal. In addition, we propose feasible FDF tests with good asymptotic and finite sample properties.

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File URL: http://ftp.itam.mx/pub/academico/inves/lobato/04-01.pdf
File Function: First version, 2004
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Paper provided by Centro de Investigacion Economica, ITAM in its series Working Papers with number 0401.

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Length: 29 pages
Date of creation: Feb 2004
Date of revision:
Handle: RePEc:cie:wpaper:0401
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  1. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  2. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  3. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
  4. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
  5. Peter M Robinson & Carlos Velasco, 2000. "Whittle Pseudo-Maximum Likelihood Estimation for Nonstationary Time Series - (Now published in Journal of the American Statistical Association, 95, (2000), pp.1229-1243.)," STICERD - Econometrics Paper Series /2000/391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  7. Delgado, Miguel A. & Velasco, Carlos, 2005. "Sign tests for long-memory time series," Journal of Econometrics, Elsevier, vol. 128(2), pages 215-251, October.
  8. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August.
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