Nonparametric regression for locally stationary functional time series

Abstract
In this study, we develop an asymptotic theory of nonparametric regression for locally stationary functional time series. First, we introduce a notion of 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 and the Nadaraya-Watson (NW) estimator of the regression function, and a central limit theorem of the NW estimator.
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