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New Fractional Dickey and Fuller Test

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  • Bensalma, Ahmed

Abstract

The aim of this paper is motivated by the following question: “If a series were best characterized by fractional process, would a researcher be able to detect that fact by using conventional Dickey-Fuller (1979) test?” To answer this question, in simple framework, we propose a new fractional Dickey-Fuller (F-DF) test, different from the test of Dolado, Gonzalo and Mayoral (2002).

Suggested Citation

  • Bensalma, Ahmed, 2015. "New Fractional Dickey and Fuller Test," MPRA Paper 65282, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:65282
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    File URL: https://mpra.ub.uni-muenchen.de/65282/1/MPRA_paper_65282.pdf
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    References listed on IDEAS

    as
    1. Johansen, Søren & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
    2. Dickey, David A & Pantula, Sastry G, 1987. "Determining the Ordering of Differencing in Autoregressive Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 455-461, October.
    3. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    4. Ignacio N. Lobato & Carlos Velasco, 2006. "Optimal Fractional Dickey-Fuller tests," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 492-510, November.
    5. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
    6. Diebold, Francis X. & Rudebusch, Glenn D., 1991. "On the power of Dickey-Fuller tests against fractional alternatives," Economics Letters, Elsevier, vol. 35(2), pages 155-160, February.
    7. Juan J. Dolado & Jesus Gonzalo & Laura Mayoral, 2002. "A Fractional Dickey-Fuller Test for Unit Roots," Econometrica, Econometric Society, vol. 70(5), pages 1963-2006, September.
    8. Ignacio N Lobato & Carlos Velasco, 2007. "Efficient Wald Tests for Fractional Unit Roots," Econometrica, Econometric Society, vol. 75(2), pages 575-589, March.
    9. Bensalma, Ahmed, 2013. "Simple Fractional Dickey Fuller test," MPRA Paper 50315, University Library of Munich, Germany.
    10. Ahmed Bensalma, 2016. "A consistent test for unit root against fractional alternative," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 27(1/2), pages 252-274.
    11. Liu, Ming, 1998. "Asymptotics Of Nonstationary Fractional Integrated Series," Econometric Theory, Cambridge University Press, vol. 14(5), pages 641-662, October.
    12. Li, Hongyi, 1995. "A Reexamination of the Nelson-Plosser Data Set Using Recursive and Sequential Tests," Empirical Economics, Springer, vol. 20(3), pages 501-518.
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    More about this item

    Keywords

    Fractional unit root; Dickey-Fuller Test; Fractional integration parameter.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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