Work

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

Year: 2026

Type: article

Abstract: 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.

Source: Mathematics

DOI: 10.3390/math14091455

Authors: Salim Bouzebda, Mohammed B. Alamari, Fatimah A. Almulhim, Ali Laksaci

Institutions: Université de Technologie de Compiègne, Laboratoire de mathématiques appliquées de Compiègne, King Khalid University, Princess Nourah bint Abdulrahman University

Language: English

Topic: Advanced Statistical Methods and Models

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Princess Nourah Bint Abdulrahman University, King Khalid University