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.

翻译：在本研究中,我们为当地固定功能时间序列开发了非参数回归的无参数理论。 首先,我们引入了当地固定功能时间序列的概念,该功能序列在半计量空间中取值。 然后,我们为LSFTS提出了一个非参数模型,该模型的回归函数随时间而平稳变化。我们为一组内核测量员、Nadaraya-Watson(NW)的回归函数测量员以及NWS测量员的中央限值确定了统一的趋同率。