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Efficient Wald Tests for Fractional Unit Roots

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Author Info
Ignacio N Lobato
Carlos Velasco

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Abstract

In this article we introduce efficient Wald tests for testing the null hypothesis of the unit root against the alternative of the fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson Lagrange multiplier tests. Our results contrast with the tests for fractional unit roots, introduced by Dolado, Gonzalo, and Mayoral, 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 preestimation of short or long memory parameters. Copyright The Econometric Society 2007.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2006.00758.x
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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 75 (2007)
Issue (Month): 2 (03)
Pages: 575-589
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Handle: RePEc:ecm:emetrp:v:75:y:2007:i:2:p:575-589

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
  3. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(04), pages 549-582, August. [Downloadable!]
  4. Breitung, Jorg & Hassler, Uwe, 2002. "Inference on the cointegration rank in fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 167-185, October. [Downloadable!] (restricted)
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  5. Delgado, Miguel A. & Velasco, Carlos, 2005. "Sign tests for long-memory time series," Journal of Econometrics, Elsevier, vol. 128(2), pages 215-251, October. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. Peter M. Robinson & Javier Hualde, 2002. "Cointegration in Fractional Systems with Unknown Integration Orders," Faculty Working Papers 07/02, School of Economics and Business Administration, University of Navarra. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Peter Sephton, 2008. "Critical values of the augmented fractional Dickey–Fuller test," Empirical Economics, Springer, vol. 35(3), pages 437-450, November. [Downloadable!] (restricted)
  2. Søren Johansen & Morten Ørregaard Nielsen, 2007. "Likelihood inference for a nonstationary fractional autoregressive model," CREATES Research Papers 2007-33, School of Economics and Management, University of Aarhus. [Downloadable!]
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  3. Juan Jose Dolado & Jesus Gonzalo & Laura Mayoral, 2008. "Simple Wald tests of the fractional integration parameter : an overview of new results," Economics Working Papers we20080129, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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