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ARFIMA Process : Tests and Applications at a White Noise Process, A Random Walk Process and the Stock Exchange Index CAC 40

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  • Régis Bourbonnais

    (LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Magda Mara Maftei

    (A.S.E. - The Bucharest Academy of Economic Studies / Academia de Studii Economice din Bucureşti)

Abstract

The assumption of linearity is implicitly accepted in the process which generates a time series condition submitted to a ARIMA. That is why, in this paper, we shall discuss the research of long memory in the processes: the fractional ARIMA models, denoted as ARFIMA, where d and D, the degree of differentiation of the filters is not integer. After presenting the characteristics of the ARFIMA process, we shall discuss the long-memory tests (statistics rescaled Range Lo and R/S* Moody and Wu). Finally three examples and tests on a white noise process, a random walk model and the stock index of Paris Stock Exchange (CAC40) will illustrate the method.

Suggested Citation

  • Régis Bourbonnais & Magda Mara Maftei, 2012. "ARFIMA Process : Tests and Applications at a White Noise Process, A Random Walk Process and the Stock Exchange Index CAC 40," Post-Print hal-01491880, HAL.
    • Handle: RePEc:hal:journl:hal-01491880
    Note: View the original document on HAL open archive server: https://hal.science/hal-01491880
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    References listed on IDEAS

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    1. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    2. Clifford M. Hurvich & Bonnie K. Ray, 1995. "Estimation Of The Memory Parameter For Nonstationary Or Noninvertible Fractionally Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(1), pages 17-41, January.
    3. Ray, Bonnie K., 1993. "Long-range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model," International Journal of Forecasting, Elsevier, vol. 9(2), pages 255-269, August.
    4. Uwe Hassler, 1993. "Regression Of Spectral Estimators With Fractionally Integrated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(4), pages 369-380, July.
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    Cited by:

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    2. Fernando Zarzosa Valdivia, 2020. "Inflation Dynamics in the ABC (Argentina, Brazil and Chile) countries," Ensayos de Política Económica, Departamento de Investigación Francisco Valsecchi, Facultad de Ciencias Económicas, Pontificia Universidad Católica Argentina., vol. 3(2), pages 77-99, Octubre.

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