Functional principal component analysis (FPCA) has played an important role in the development of functional time series analysis. This paper 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 some essential properties of cointegrated functional time series. As an empirical illustration, our methodology is applied to two empirical examples: age-specific employment rates and earning densities.

翻译：功能主要组成部分分析(FPCA)在发展功能时间序列分析方面发挥了重要作用,本文件探讨了如何利用FPCA分析共同整合功能时间序列,并提议修改FPCA,将其作为新的统计工具。我们修改过的FPCA不仅为组合矢量提供了无症状、效率更高的估算器,而且导致基于FPCA的新型测试,以检查组合功能时间序列的某些基本特性。作为经验性例证,我们的方法适用于两个经验性实例:特定年龄就业率和收入密度。