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Fractional Dickey-Fuller test with or without prehistorical influence

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  • BENSALMA, Ahmed

Abstract

Recently the generalization of the standard Dickey-Fuller test to the fractional case has been proposed. The proposed test, called fractional Dickey-Fuller test can be applied to sample generated from a type I or a type II fractional process. Depending on whether the test is applied to sample generated from a type I or type II process, it is referred to as a test with or without prehistoric influence respectively. The main and the first objective of this paper is to study the impact induced by a pre-sample of the finite sample null distribution. In fact, the recently proposed test is built based on a composite null hypothesis rather than a sample one. The second objective is to highlight the theoretical justifications for the choice of the null composite hypothesis. All the theoretical results are illustrated with simulated and real data sets. Furthermore, to facilitate the reproducibility of our simulation data and figures we provide all the necessary supplementary material consisting of EViews programs.

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  • BENSALMA, Ahmed, 2021. "Fractional Dickey-Fuller test with or without prehistorical influence," MPRA Paper 107408, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:107408
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    File URL: https://mpra.ub.uni-muenchen.de/107408/1/MPRA_paper_107408.pdf
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    References listed on IDEAS

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    1. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(1), pages 95-131, April.
    2. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    3. Tanaka, Katsuto, 1999. "The Nonstationary Fractional Unit Root," Econometric Theory, Cambridge University Press, vol. 15(4), pages 549-582, August.
    4. 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.
    5. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
    6. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    7. Wang, Qiying & Lin, Yan-Xia & Gulati, Chandra M., 2003. "Asymptotics For General Fractionally Integrated Processes With Applications To Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(1), pages 143-164, February.
    8. 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.
    9. Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(2), pages 256-271, August.
    10. Bensalma, Ahmed, 2021. "An Eviews program to perform the fractional Dickey-Fuller test," MPRA Paper 107445, University Library of Munich, Germany.
    11. Liu, Ming, 1998. "Asymptotics Of Nonstationary Fractional Integrated Series," Econometric Theory, Cambridge University Press, vol. 14(5), pages 641-662, October.
    12. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
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    1. Bensalma, Ahmed, 2021. "An Eviews program to perform the fractional Dickey-Fuller test," MPRA Paper 107445, University Library of Munich, Germany.

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    More about this item

    Keywords

    ARFIMA; fractional integration; Dickey-Fuller test; Fractional Dickey-Fuller test; type I and type II fractional Brownian motion.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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