Fractional time series modelling

Wai Keung LI, A. I. MCLEOD

Research output: Contribution to journalArticlespeer-review

120 Citations (Scopus)


Aspects of model building using fractionally differenced autoregressive-moving average processes are discussed. An algorithm for approximate maximum likelihood estimation is outlined and the large-sample distribution of the maximum likelihood estimates is derived. The large-sample distribution of the residual autocorrelations is also derived and a modified portmanteau test statistic is obtained for checking model adequacy. Copyright © 1986 Oxford University Press on behalf of Biometrika Trust.
Original languageEnglish
Pages (from-to)217-221
Issue number1
Publication statusPublished - Apr 1986


Li, W. K., & McLeod, A. I. (1986). Fractional time series modelling. Biometrika, 73(1), 217-221. doi: 10.1093/biomet/73.1.217


  • Fractional differencing
  • Long-memory time series
  • Maximum likelihood
  • Parsimony
  • Portmanteau test
  • Residual autocorrelation

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