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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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    References listed on IDEAS

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    10. 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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    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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