Functional principal component analysis (FPCA) has played an important role in the development of functional time series (FTS) analysis. This paper investigates how FPCA can be used to analyze cointegrated functional time series and propose 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 KPSS-type tests for examining some essential properties of cointegrated  time series. As an empirical illustration, our methodology is applied to the time series of log-earning densities.
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.
D
(FTS)
R
propose
proposes
R
KPSS-type
FPCA-based
A
functional
R
the time series of log-earning
two empirical examples: age-specific employment rates and earning