Abstract
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.
Funding Statement
D. Kurisu is partially supported by JSPS KAKENHI Grant Number 20K13468.
Acknowledgments
The author would like to thank the Editor Domenico Marinucci, the AE, and a referee for their constructive comments that helped improve the quality of the paper. The author also would like to thank Taisuke Otsu for his helpful comments.
Citation
Daisuke Kurisu. "Nonparametric regression for locally stationary functional time series." Electron. J. Statist. 16 (2) 3973 - 3995, 2022. https://doi.org/10.1214/22-EJS2041
Information
