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Efficient Wald Tests For Fractional Unit Roots

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  • Ignacio N. Lobato

    ()

  • Carlos Velasco

    ()

Abstract

In this article we introduce efficient Wald tests for testing the null hypothesis of unit root against the alternative of fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson (1991, 1994a) Lagrange Multiplier tests. Our results contrast with the tests for fractional unit roots introduced by Dolado, Gonzalo and Mayoral (2002) which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first order asymptotic properties of the proposed tests are not affected by the pre-estimation of short or long memory parameters

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Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we056935.

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Date of creation: Nov 2005
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Handle: RePEc:cte:werepe:we056935

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  1. Jeffrey M. Wooldridge, 2001. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262232197, December.
  2. Breitung, Jorg & Hassler, Uwe, 2002. "Inference on the cointegration rank in fractionally integrated processes," Journal of Econometrics, Elsevier, Elsevier, vol. 110(2), pages 167-185, October.
  3. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2003/449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, Elsevier, vol. 47(1), pages 67-84, January.
  5. Delgado, Miguel A. & Velasco, Carlos, 2005. "Sign tests for long-memory time series," Journal of Econometrics, Elsevier, Elsevier, vol. 128(2), pages 215-251, October.
  6. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 15(04), pages 549-582, August.
  7. 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, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2000/391, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, Elsevier, vol. 91(2), pages 325-371, August.
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