Nonparametric regression for locally stationary functional time series

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