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Parametric estimation for ARFIMA models via spectral methods

Author

Listed:
  • Mauro Coli

    (University “G. D'Annunzio”)

  • Lara Fontanella

    (University “G. D'Annunzio”)

  • Mariagrazia Granturco

    (University “G. D'Annunzio”)

Abstract

Given a fractional integrated, autoregressive, moving average,ARFIMA (p, d, q) process, the simultaneous estimation of the short and long memory parameters can be achieved by maximum likelihood estimators. In this paper, following a two-step algorithm, the coefficients are estimated combining the maximum likelihood estimators with the general orthogonal decomposition of stochastic processes. In particular, the principal component analysis of stochastic processes is exploited to estimate the short memory parameters, which are plugged into the maximum likelihood function to obtain the fractional differencingd.

Suggested Citation

  • Mauro Coli & Lara Fontanella & Mariagrazia Granturco, 2005. "Parametric estimation for ARFIMA models via spectral methods," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(1), pages 11-27, February.
    • Handle: RePEc:spr:stmapp:v:14:y:2005:i:1:d:10.1007_bf02511572
    DOI: 10.1007/BF02511572
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    References listed on IDEAS

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    1. 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.
    2. Ignacio N. Lobato & Peter M. Robinson, 1998. "A Nonparametric Test for I(0)," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 475-495.
    3. Cheung, Yin-Wong & Diebold, Francis X., 1994. "On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean," Journal of Econometrics, Elsevier, vol. 62(2), pages 301-316, June.
    4. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    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.
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