Functional principal component analysis (FPCA) has played an important role in the development of functional time series analysis. This note investigates how FPCA can be used to analyze cointegrated functional time series and proposes a modification of FPCA as a novel statistical tool. Our modified FPCA not only provides an asymptotically more efficient estimator of the cointegrating vectors, but also leads to novel FPCA-based tests for examining essential properties of cointegrated functional time series.

翻译：函数主成分分析（FPCA）在函数时间序列分析的发展中发挥了重要作用。本文探讨了如何利用FPCA分析共积分函数时间序列，并提出了一种基于FPCA改进的新型统计工具。改进后的FPCA不仅能够提供渐近更高效的共积分向量估计量，还能衍生出基于FPCA的新颖检验方法，用于考察共积分函数时间序列的基本性质。