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Estimation of the memory parameter by fitting fractionally differenced autoregressive models

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  • Bhansali, R.J.
  • Giraitis, L.
  • Kokoszka, P.S.

Abstract

Estimation of the memory parameter, d, by fitting a fractionally differenced autoregression of order p, where p approaches infinity simultaneously with the observed series length, n, is examined. Under some conditions on growth of p with respect to n and on the short-memory component, which admits an infinite autoregressive representation with coefficients aj, the estimator is shown to be consistent and asymptotically normal, where p may be taken to be proportional to logn. The joint asymptotic distribution of the estimators of d and of the aj is also derived.

Suggested Citation

  • Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2006. "Estimation of the memory parameter by fitting fractionally differenced autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2101-2130, November.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:10:p:2101-2130
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    References listed on IDEAS

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    1. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
    2. Clifford M. Hurvich & Julia Brodsky, 2001. "Broadband Semiparametric Estimation of the Memory Parameter of a Long‐Memory Time Series Using Fractional Exponential Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(2), pages 221-249, March.
    3. Eric Moulines & Philippe Soulier, 2000. "Data Driven Order Selection for Projection Estimator of the Spectral Density of Time Series with Long Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(2), pages 193-218, March.
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    Cited by:

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    2. Uwe Hassler & Marc-Oliver Pohle, 2019. "Forecasting under Long Memory and Nonstationarity," Papers 1910.08202, arXiv.org.

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