Single index regression for locally stationary functional time series

Breix Michael Agua; Salim Bouzebda; Breix Michael Agua; Salim Bouzebda

doi:10.3934/math.20241719

AIMS Mathematics

2024, Volume 9, Issue 12: 36202-36258. doi: 10.3934/math.20241719

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Single index regression for locally stationary functional time series

Breix Michael Agua ^1,2,
Salim Bouzebda ^{1
,
,}

1.
Université de technologie de Compiègne, Laboratory of Applied Mathematics of Compiègne (LMAC), CS 60319 - 57 avenue de Landshut, Compiègne, France
2.
Department of Mathematics, Caraga State University, Butuan City, Philippines

Received: 11 September 2024 Revised: 04 December 2024 Accepted: 09 December 2024 Published: 30 December 2024
MSC : 60F05, 62F40, 60G15, 60K05, 60K15

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.
- convergence rates,
- exponential inequality,
- kernel regression,
- functional time series,
- locally stationary process,
- single index model,
- functional data analysis
Citation: Breix Michael Agua, Salim Bouzebda. Single index regression for locally stationary functional time series[J]. AIMS Mathematics, 2024, 9(12): 36202-36258. doi: 10.3934/math.20241719

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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.

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