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)在函数型时间序列分析的发展中扮演重要角色。本文探讨了如何运用FPCA分析协整函数型时间序列，并提出了一种改进的FPCA作为一种新型统计工具。改进后的FPCA不仅提供了协整向量的渐近更高效估计量，还催生了基于FPCA的新型检验方法，用于考察协整函数型时间序列的基本性质。