A subset of long-range dependent FARIMA processes is considered. A method for estimating the parameter that describes the long-range dependency of such a process is suggested. The method is based on an asymptotic expression for the covariance function of the process and gives a closed form solution by means of a weighted linear least squares estimate. The variance of the estimate given by themethod is analyzed and, at the same time, the optimal choice of the weighting is expressed. A numerical illustration of the method and the material in the paper is provided.
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