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Estimation of the memory parameter by fitting fractionally differenced autoregressive models


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


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

    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.
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