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：功能主成分分析在协整函数时间序列中的应用 功能主成分分析 (FPCA) 在函数时间序列分析的发展中扮演着重要角色。本文研究了 FPCA 如何用于分析协整函数时间序列，并提出了一种修改版的 FPCA 作为一种新的统计工具。我们改进的 FPCA 不仅提供了协整向量的渐近更高效的估计器，而且还引导出基于 FPCA 的测试以检查协整函数时间序列的基本特性。