Seasonal functional autoregressive models

Atefeh Zamani, Hossein Haghbin, Maryam Hashemi, Rob J. Hyndman

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


Functional autoregressive models are popular for functional time series analysis, but the standard formulation fails to address seasonal behaviour in functional time series data. To overcome this shortcoming, we introduce seasonal functional autoregressive time series models. For the model of order one, we derive sufficient stationarity conditions and limiting behaviour, and provide estimation and prediction methods. Moreover, we consider a portmanteau test for testing the adequacy of this model, and we derive its asymptotic distribution. The merits of this model are demonstrated using simulation studies and via an application to hourly pedestrian counts.

Original languageEnglish
Pages (from-to)197-218
Number of pages22
JournalJournal of Time Series Analysis
Issue number2
Publication statusPublished - Mar 2022


  • central limit theorem
  • estimation
  • Functional time series analysis
  • prediction
  • seasonal functional autoregressive model

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