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A Note On Long Memory Time Series

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  • Claude Diebolt
  • Vivien Guiraud

Abstract

This note presents the fractional integrated processes which are the main models used to describe long memory phenomena. Section 1 briefly defines the concept of fractional integration, shows the fundamental properties and provides a short summary of the estimation methods. Section 2 consists of a survey of their extensions in order to model long-term cycles.
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  • Claude Diebolt & Vivien Guiraud, 2005. "A Note On Long Memory Time Series," Quality & Quantity: International Journal of Methodology, Springer, vol. 39(6), pages 827-836, December.
    • Handle: RePEc:spr:qualqt:v:39:y:2005:i:6:p:827-836
    DOI: 10.1007/s11135-004-0436-z
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    1. Beran, Jan, 1999. "SEMIFAR Models - A Semiparametric Framework for Modelling Trends, Long Range Dependence and Nonstationarity," CoFE Discussion Papers 99/16, University of Konstanz, Center of Finance and Econometrics (CoFE).
    2. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
    3. 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.
    4. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    5. Gemai Chen & Bovas Abraham & Shelton Peiris, 1994. "Lag Window Estimation Of The Degree Of Differencing In Fractionally Integrated Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 473-487, September.
    6. Valderio A. Reisen, 1994. "ESTIMATION OF THE FRACTIONAL DIFFERENCE PARAMETER IN THE ARIMA(p, d, q) MODEL USING THE SMOOTHED PERIODOGRAM," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 335-350, May.
    7. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
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    Cited by:

    1. ERER, Deniz & ERER, Elif & GÜLEÇ, Tuna Can, 2016. "Fractional Cointegration Analysis Of Stock Market And Exchange Rates: The Case Of Turkey," Studii Financiare (Financial Studies), Centre of Financial and Monetary Research "Victor Slavescu", vol. 20(3), pages 80-94.
    2. Roy Cerqueti & Giulia Rotundo, 2015. "A review of aggregation techniques for agent-based models: understanding the presence of long-term memory," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(4), pages 1693-1717, July.
    3. Claude Diebolt & Cédric Doliger, 2008. "New international evidence on the cyclical behaviour of output: Kuznets swings reconsidered," Quality & Quantity: International Journal of Methodology, Springer, vol. 42(6), pages 719-737, December.
    4. Claude Diebolt & Karine Pellier, 2008. "Analyse spectrale de l’évolution de longue période des brevets en France, en Allemagne, en Grande-Bretagne, aux Etats-Unis et au Japon (17ème-20ème siècles)," Working Papers 08-09, Association Française de Cliométrie (AFC).
    5. Mansour Zarra-Nezhad & Ali Raoofi & Mohammad Hadi Akbarzdeh, 2016. "The Existence of Long Memory Property in OPEC Oil Prices," Asian Journal of Economic Modelling, Asian Economic and Social Society, vol. 4(3), pages 142-152, September.

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    Keywords

    fractional integration; long memory;

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