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A generalized fractionally differencing approach in long-memory modeling. (English) Zbl 0837.62066

Lith. Math. J. 35, No. 1, 53-65 (1995) and Liet. Mat. Rink. 35, No. 1, 65-81 (1995).
Summary: We extend the class of fractional ARIMA models to the class of fractional ARUMA models, which describe long-memory time series with long-range periodical behavior at a finite number of spectrum frequencies. The exact asymptotics of the covariance function and the spectrum at the points of peaks and zeros are given. To obtain asymptotic expansions, Gegenbauer polynomials are used. Consistent parameter estimation is discussed using Whittle’s estimate.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15 Inference from stochastic processes and spectral analysis
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