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Estimation of the long memory parameter by fitting fractionally differenced autoregressive models

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  • R J Bhansali
  • L Giraitis
  • P Kokoszka

Abstract

We examine the estimation of the memory parameter d of I(d) series, by fitting an auto-regressive AR(k) representation where k approaches infinity simultaneously with the observed series length n. Under some conditions on the growth of k with respect to n, and on the short memory component of the spectral density which admits an infinite autoregressive representation, the estimator is shown to be ?(k/n) consistent and asymptotically normal, where k may be taken to be proportional to log n. The joint asymptotic distribution of the long memory parameter and the estimated autoregressive coefficients (increasing in number) is derived.

Suggested Citation

  • R J Bhansali & L Giraitis & P Kokoszka, "undated". "Estimation of the long memory parameter by fitting fractionally differenced autoregressive models," Discussion Papers 05/20, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:05/20
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    Cited by:

    1. Hurvich, Clifford M. & Moulines, Eric & Soulier, Philippe, 2002. "The FEXP estimator for potentially non-stationary linear time series," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 307-340, February.

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