Principal Components Analysis of Periodically Correlated Functional Time Series
针对周期相关的函数型时间序列，定义了主成分分析中的周期算子值滤波器、得分过程及反演公式，并证明了其最优性。通过R包实现，模拟和实例表明该方法优于现有工具。
Within the framework of functional data analysis, we develop principal component analysis for periodically correlated time series of functions. We define the components of the above analysis including periodic operator‐valued filters, score processes, and the inversion formulas. We show that these objects are defined via a convergent series under a simple condition requiring summability of the Hilbert–Schmidt norms of the filter coefficients and that they possess optimality properties. We explain how the Hilbert space theory reduces to an approximate finite‐dimensional setting which is implemented in a custom‐build |R| package. A data example and a simulation study show that the new methodology is superior to existing tools if the functional time series exhibits periodic characteristics.