Before revision:  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.
After revision:  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 functional time series.