Quantifying the serial correlation across time lags is a crucial step in the identification and diagnosis of a time series model. Simple and partial autocorrelation functions of the time series are the most widely used tools for this purpose with scalar time series. Nevertheless, there is a lack of an established method for the identification of functional time series (FTS) models. Functional versions of the autocorrelation and partial autocorrelation functions for FTS based on the L2 norm of the lagged autocovariance operators of the series are proposed. Diagnostic plots of these functions coupled with prediction bounds derived from large sample results for the autocorrelation and partial autocorrelation functions estimated from a strong functional white noise series are proposed as fast and efficient tools for selecting the order and assessing the adequacy of functional SARMAX models. These methods are studied in numerical simulations with both white noise and serially correlated functional processes, which show that the structure of the processes can be well identified using the proposed techniques. The applicability of the method is illustrated with two real-world datasets: Eurodollar futures contracts and electricity price profiles.

中文翻译：

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通过自相关和偏自相关分析进行功能时间序列模型识别和诊断

量化跨时间滞后的序列相关性是识别和诊断时间序列模型的关键步骤。时间序列的简单和偏自相关函数是用于标量时间序列的最广泛使用的工具。然而，缺乏用于识别功能时间序列（FTS）模型的既定方法。提出了基于系列滞后自协方差算子的 L2 范数的 FTS 自相关和偏自相关函数的函数版本。这些函数的诊断图与从强函数白噪声序列估计的自相关和偏自相关函数的大样本结果得出的预测边界相结合，被提议作为快速有效的工具，用于选择阶数和评估函数 SARMAX 模型的充分性。这些方法在具有白噪声和序列相关功能过程的数值模拟中进行了研究，这表明使用所提出的技术可以很好地识别过程的结构。该方法的适用性通过两个真实世界的数据集来说明：欧洲美元期货合约和电价概况。这表明使用所提出的技术可以很好地识别过程的结构。该方法的适用性通过两个真实世界的数据集来说明：欧洲美元期货合约和电价概况。这表明使用所提出的技术可以很好地识别过程的结构。该方法的适用性通过两个真实世界的数据集来说明：欧洲美元期货合约和电价概况。