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 behavior, and provide estimation and prediction methods. Some properties of the general order $P$ model are also presented. The merits of these models are demonstrated using simulation studies and via an application to real data.
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