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Optimal Fractional Dickey-Fuller tests

Author

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  • Ignacio N. Lobato
  • Carlos Velasco

Abstract

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

Suggested Citation

  • 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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    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. Dolado Juan J. & Gonzalo Jesus & Mayoral Laura, 2008. "Wald Tests of I(1) against I(d) Alternatives: Some New Properties and an Extension to Processes with Trending Components," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(4), pages 1-35, December.
    5. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    6. Lasak, Katarzyna, 2010. "Likelihood based testing for no fractional cointegration," Journal of Econometrics, Elsevier, vol. 158(1), pages 67-77, September.
    7. 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 School of Economics.
    8. Bensalma, Ahmed, 2015. "New Fractional Dickey and Fuller Test," MPRA Paper 65282, University Library of Munich, Germany.
    9. Lobato, Ignacio N. & Velasco, Carlos, 2008. "Power comparison among tests for fractional unit roots," Economics Letters, Elsevier, vol. 99(1), pages 152-154, April.
    10. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2024. "Partially one-sided semiparametric inference for trending persistent and antipersistent processes," Econometrics and Statistics, Elsevier, vol. 30(C), pages 1-14.
    11. Federico Carlini & Katarzyna (K.A.) Lasak, 2018. "Likelihood based inference for an Identifiable Fractional Vector Error Correction Model," Tinbergen Institute Discussion Papers 18-085/III, Tinbergen Institute.
    12. 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.
    13. 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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