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Revisiting the Autocorrelation of Long Memory Time Series Models

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  • Shelton Peiris

    (School of Mathematics and Statistics, University of Sydney, Camperdown, NSW 2006, Australia
    These authors contributed equally to this work.)

  • Richard Hunt

    (School of Mathematics and Statistics, University of Sydney, Camperdown, NSW 2006, Australia
    These authors contributed equally to this work.)

Abstract

In this article we first revisit some earlier work on fractionally differenced white noise and correct some issues with previously published formulae. We then look at vector processes and derive formula for the Autocorrelation function, which is extended in this work to a larger range of parameter values than considered elsewhere, and compare this with previously published work.

Suggested Citation

  • Shelton Peiris & Richard Hunt, 2023. "Revisiting the Autocorrelation of Long Memory Time Series Models," Mathematics, MDPI, vol. 11(4), pages 1-8, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:817-:d:1059071
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    References listed on IDEAS

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    1. Luis Alberiko Gil-Alana & Zeynel Abidin Ozdemir & Aysit Tansel, 2019. "Long Memory in Turkish Unemployment Rates," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 55(1), pages 201-217, January.
    2. Stefanos Kechagias & Vladas Pipiras, 2015. "Definitions And Representations Of Multivariate Long-Range Dependent Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 1-25, January.
    3. John Haslett & Adrian E. Raftery, 1989. "Space‐Time Modelling with Long‐Memory Dependence: Assessing Ireland's Wind Power Resource," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(1), pages 1-21, March.
    4. John Barkoulas & Walter C. Labys & Joseph Onochie, 1997. "Fractional dynamics in international commodity prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(2), pages 161-189, April.
    5. 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.
    6. Pascal Bondon & Wilfredo Palma, 2007. "A Class of Antipersistent Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 261-273, March.
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    Cited by:

    1. Xuyan Xiang & Jieming Zhou, 2023. "An Excess Entropy Approach to Classify Long-Term and Short-Term Memory Stationary Time Series," Mathematics, MDPI, vol. 11(11), pages 1-16, May.

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