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.

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非参数理论。 首先,我们引入了当地固定功能时间序列的概念(LSFTS),它包含半计量空间的值。然后,我们为LSFTS提出了一个非参数模型,其回归函数随时间而平稳变化。我们为一组内核测算员和Nadaraya-Watson(NW)测算员确定了统一的回归函数趋同率,并为NW测算员确定了一个中心限值理论。