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Optimal Fractional Dickey-Fuller tests


  • Ignacio N. Lobato
  • Carlos Velasco


This article analyzes the fractional Dickey-Fuller (FDF) test for unit roots recently introduced by Dolado, Gonzalo and Mayoral (2002 Econometrica 70, 1963--2006) within a more general setup. These authors motivate their test with a particular analogy with the Dickey-Fuller test, whereas we interpret the FDF test as a class of tests indexed by an auxiliary parameter, which can be chosen to maximize the power of the test. Within this framework, we investigate optimality aspects of the FDF test and show that the version of the test proposed by these authors is not optimal. For the white noise case, we derive simple optimal FDF tests based on consistent estimators of the true degree of integration. For the serial correlation case, optimal augmented FDF (AFDF) tests are difficult to implement since they depend on the short-term component. Hence, we propose a feasible procedure that automatically optimizes a prewhitened version of the AFDF test and avoids this problem. Copyright Royal Economic Society 2006

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  • Ignacio N. Lobato & Carlos Velasco, 2006. "Optimal Fractional Dickey-Fuller tests," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 492-510, November.
  • Handle: RePEc:ect:emjrnl:v:9:y:2006:i:3:p:492-510

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    References listed on IDEAS

    1. Andrés González & Timo Teräsvirta & Dick van Dijk & Yukai Yang, 1910. "Panel Smooth Transition Regression Models," CREATES Research Papers 2017-36, Department of Economics and Business Economics, Aarhus University.
    2. Hansen, Bruce E., 1999. "Threshold effects in non-dynamic panels: Estimation, testing, and inference," Journal of Econometrics, Elsevier, vol. 93(2), pages 345-368, December.
    3. Hansen, Bruce E, 1999. " Testing for Linearity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(5), pages 551-576, December.
    4. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
    5. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    6. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(03), pages 315-352, June.
    7. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    8. Strikholm, Birgit & Teräsvirta, Timo, 2005. "Determining the Number of Regimes in a Threshold Autoregressive Model Using Smooth Transition Autoregressions," SSE/EFI Working Paper Series in Economics and Finance 578, Stockholm School of Economics, revised 11 Feb 2005.
    9. George Kapetanios, 2003. "Threshold models for trended time series," Empirical Economics, Springer, vol. 28(4), pages 687-707, November.
    10. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    11. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    12. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    13. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(01), pages 17-43, March.
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    Cited by:

    1. Davidson, James & Monticini, Andrea, 2010. "Tests for cointegration with structural breaks based on subsamples," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2498-2511, November.
    2. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
    3. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2017. "Quasi-maximum likelihood estimation and bootstrap inference in fractional time series models with heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 198(1), pages 165-188.
    4. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    5. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2003. "Testing for a Unit Root Against Fractional Alternatives in the Presence of a Maintained Trend," Working Papers 29, Barcelona Graduate School of Economics.
    6. Bensalma, Ahmed, 2015. "New Fractional Dickey and Fuller Test," MPRA Paper 65282, University Library of Munich, Germany.
    7. Lobato, Ignacio N. & Velasco, Carlos, 2008. "Power comparison among tests for fractional unit roots," Economics Letters, Elsevier, vol. 99(1), pages 152-154, April.
    8. Dolado, Juan José & Gonzalo, Jesús & Mayoral, Laura, 2008. "Simple Wald tests of the fractional integration parameter : an overview of new results," UC3M Working papers. Economics we20080129, Universidad Carlos III de Madrid. Departamento de Economía.
    9. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.

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