Estimation of the memory parameter by fitting fractionally differenced autoregressive models
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.
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Volume (Year): 97 (2006)
Issue (Month): 10 (November)
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- 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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