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.

中文翻译：

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季节性函数自回归模型

功能自回归模型在功能时间序列分析中很受欢迎，但标准公式未能解决功能时间序列数据中的季节性行为。为了克服这个缺点，我们引入了季节性函数自回归时间序列模型。对于一阶模型，我们推导出了足够的平稳性条件和限制行为，并提供了估计和预测方法。此外，我们考虑了一个 portmanteau 测试来测试这个模型的充分性，我们推导出它的渐近分布。该模型的优点通过模拟研究和每小时行人计数的应用得到证明。