Single index regression for locally stationary functional time series

Single index regression for locally stationary functional time series

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 convergenc...

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Bibliographic Details
Main Authors: Breix Michael Agua, Salim Bouzebda
Format: Article
Language:English
Published: AIMS Press 2024-12-01
Series:AIMS Mathematics
Subjects:
convergence rates
exponential inequality
kernel regression
functional time series
locally stationary process
single index model
functional data analysis
Online Access:https://www.aimspress.com/article/doi/10.3934/math.20241719
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Summary: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.
ISSN:2473-6988

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