Nonparametric econometrics with fractional and long-memory regressors

Ciprian A. Tudor

DOI: 10.63065/ajafe.2026.1.001

Email: ciprian.tudor@univ-lille.fr

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Ngày nhận bài: 09/09/2026

Ngày nhận bài sửa: 09/09/2026

Ngày duyệt đăng: 09/09/2026

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Tóm tắt

Purpose – This paper surveys advances in nonparametric regression models with long-memory regressors, particularly those driven by fractional Brownian motion, and examines how persistence affects econometric inference.

Design/methodology/approach – A theoretical survey is conducted on kernel-based nonparametric estimators when regressors follow fractional stochastic processes. The analysis relies on asymptotic methods and incorporates tools such as local time techniques and Malliavin calculus to study estimator behavior under strong dependence.

Findings – Long-range dependence substantially alters classical nonparametric results. The Hurst parameter plays a central role in determining consistency, convergence rates, and asymptotic distributions of estimators. Standard assumptions of independence or weak dependence are no longer applicable, and the dependence structure directly impacts bandwidth selection and limiting behavior. The analysis also highlights the importance of local time in understanding estimator properties under fractional dynamics.

Originality – The paper provides a unified synthesis of recent theoretical developments at the intersection of nonparametric econometrics and fractional stochastic processes. It clarifies how long-memory features influence estimation theory and highlights key probabilistic tools for analyzing regression models with persistent regressors.

Từ khóa

Regression model, Limit theorems, Fractional Brownian motion, Econometrics

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