Article Dans Une Revue Mathematics Année : 2026

Nonparametric Functional Times Series Data Analysis by kNN–Local Linear M-Regression

Résumé

This paper addresses the problem of nonparametric regression for functional time series, a setting complicated by the infinite-dimensional nature of the covariates, temporal dependence, and potential for outliers. We propose a new robust estimator that combines three powerful ideas: (i) k-nearest neighbors (kNN) for adaptive localization in the functional space; (ii) local linear smoothing to reduce bias; and (iii) M-estimation to ensure resilience against atypical observations. The key theoretical contribution establishes the almost-complete convergence of the proposed estimator under mild conditions that account for the functional geometry, weak dependence (via quasi-association), and robustness constraints. The obtained rate of convergence explicitly reveals the interplay between the functional concentration, dependence strength, and local smoothness of the model. A simulation study demonstrates that this method offers superior stability and predictive accuracy compared to classical alternatives, particularly under heavy-tailed errors and data contamination. The practical relevance of the approach is further illustrated through a one-step-ahead prediction application to a real-world environmental dataset of hourly NOx measurements.

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Dates et versions

hal-05605988 , version 1 (28-04-2026)

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Citer

Salim Bouzebda, Mohammed Alamari, Fatimah Almulhim, Ali Laksaci. Nonparametric Functional Times Series Data Analysis by kNN–Local Linear M-Regression. Mathematics , 2026, 14 (9), pp.1455. ⟨10.3390/math14091455⟩. ⟨hal-05605988⟩
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