A Note on Local Linear Regression for Time Series in Banach Spaces
Abstract
This work extends local linear regression to Banach space-valued time series for estimating smoothly varying means and their derivatives in non-stationary data. The asymptotic properties of both the standard and bias-reduced Jackknife estimators are analyzed under mild moment conditions, establishing their convergence rates. Simulation studies assess the finite sample performance of these estimators and compare them with the Nadaraya-Watson estimator. Additionally, the proposed methods are applied to smooth EEG recordings for reconstructing eye movements and to video analysis for detecting pedestrians and abandoned objects.
Cite
@article{arxiv.2503.15039,
title = {A Note on Local Linear Regression for Time Series in Banach Spaces},
author = {Florian Heinrichs},
journal= {arXiv preprint arXiv:2503.15039},
year = {2025}
}
Comments
Keywords: Local linear regression, Functional time series, Non-stationary time series, Kernel smoothing 18 pages, 5 figures, 4 tables