  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.
