Estimation of the memory parameter by fitting fractionally differenced autoregressive models

  • Authors:

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

  • Affiliations:

  • University of Liverpool, UK;University of York, UK;Utah State University

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2006

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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 √p/n consistent and asymptotically normal, where p may be taken to be proportional to log n. The joint asymptotic distribution of the estimators of d and of the aj is also derived.