@article{Agua2024, 
author = {Breix Michael Agua and Salim Bouzebda},
title = {Single index regression for locally stationary functional time series},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {36202-36258},
keywords = {convergence rates, exponential inequality, kernel regression, functional time series, locally stationary process, single index model, functional data analysis},
url = {https://www.sciopen.com/article/10.3934/math.20241719},
doi = {10.3934/math.20241719},
abstract = {In this research, we formulated an asymptotic theory for single index regression applied to locally stationary functional time series. Our approach involved introducing estimators featuring a regression function that exhibited smooth temporal changes. We rigorously established the uniform convergence rates for kernel estimators, specifically the Nadaraya-Watson (NW) estimator for the regression function. Additionally, we provided a central limit theorem for the NW estimator. Finally, the theory was supported by a comprehensive simulation study to investigate the finite-sample performance of our proposed method.}
}