In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally tractable algorithm to obtain the fSVD components. The effectiveness of the proposed approach is illustrated by an interesting example of remote sensing data. Also, we develop an efficient and user‐friendly R package and a shiny web application to allow interactive exploration of the results.

中文翻译：

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功能奇异谱分析

在本文中，我们开发了称为功能SSA的奇异频谱分析（SSA）的新扩展，以分析功能时间序列。通过整合功能数据分析和单变量SSA的思想来构建新方法。具体来说，我们在功能世界中引入了一个轨迹算子，它等效于常规SSA中的轨迹矩阵。在常规SSA中，需要获得轨迹矩阵的奇异值分解（SVD）才能分解给定的时间序列。由于没有提取轨迹算子的功能SVD（fSVD）的过程，因此我们引入了一种计算易处理的算法来获取fSVD分量。遥感数据的一个有趣例子说明了该方法的有效性。还，