%0 Generic
%A Giraitis, Liudas
%A Leipus, Remigijus
%C Heidelberg
%D 1993
%F heidok:21334
%R 10.11588/heidok.00021334
%T A Generalized Fractionally Differencing Approach inLong-Memory Modelling
%U https://archiv.ub.uni-heidelberg.de/volltextserver/21334/
%X We extend the class of known fractional ARIMA models to the class ofgeneralized ARIMA models which allows the generation of long-memory time serieswith long-range periodical behaviour at a finite number of spectrum frequences.The exact asymptotics of the covariance function and the spectrum at the pointsof peaks and zeroes are given. For obtaining asymptotic expansions, Gegenbauerpolynomials are used. Consistent parameter estimating is discussed using Whittle's estimate.