An introduction to long‐memory time series models and fractional differencing

C. W J Granger*, Roselyne Joyeux

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2100 Citations (Scopus)


Abstract. The idea of fractional differencing is introduced in terms of the infinite filter that corresponds to the expansion of (1‐B)d. When the filter is applied to white noise, a class of time series is generated with distinctive properties, particularly in the very low frequencies and provides potentially useful long‐memory forecasting properties. Such models are shown to possibly arise from aggregation of independent components. Generation and estimation of these models are considered and applications on generated and real data presented.

Original languageEnglish
Pages (from-to)15-29
Number of pages15
JournalJournal of Time Series Analysis
Issue number1
Publication statusPublished - 1980
Externally publishedYes


  • Fractional differencing
  • integrated models
  • long‐memory


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