  In this study, we develop an asymptotic theory of nonparametric regression
for a locally stationary functional time series. First, we introduce the notion
of a locally stationary functional time series (LSFTS) that takes values in a
semi-metric space. Then, we propose a nonparametric model for LSFTS with a
regression function that changes smoothly over time. We establish the uniform
convergence rates of a class of kernel estimators, the Nadaraya-Watson (NW)
estimator of the regression function, and a central limit theorem of the NW
estimator.
