Lithuanian Mathematical Journal

, Volume 35, Issue 1, pp 53–65 | Cite as

A generalized fractionally differencing approach in long-memory modeling

  • L. Giraitis
  • R. Leipus


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.


Time Series Parameter Estimation Asymptotic Expansion Finite Number Spectrum Frequency 
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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • L. Giraitis
  • R. Leipus

There are no affiliations available

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