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Improved estimation of drift coefficients using optimal local bandwidths

Author

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  • Christian Wiedemann

    (School of Mathematics and Science, Institute of Physics
    ForWind - Center for Wind Energy Research
    ICBM - Institute for Chemistry and Biology of the Marine Environment)

  • Matthias Wächter

    (School of Mathematics and Science, Institute of Physics
    ForWind - Center for Wind Energy Research)

  • Joachim Peinke

    (School of Mathematics and Science, Institute of Physics
    ForWind - Center for Wind Energy Research)

  • Jan A. Freund

    (School of Mathematics and Science, Institute of Physics
    ICBM - Institute for Chemistry and Biology of the Marine Environment)

Abstract

Stochastic differential equations (SDEs) are commonly used to model various systems. Data-driven methods have been widely used to estimate the drift and diffusion terms of a Langevin equation. Among the most commonly used estimation methods is the Nadaraya–Watson estimator, which is a non-parametric data-driven approach. In this study, we propose a method to improve the estimation of the drift coefficient of a stochastic process using optimal local bandwidths that minimize the error of the approximation of the first conditional moments of a univariate system. This approach is compared to a global bandwidth estimation and an estimation based on a fixed number of nearest neighbors. The proposed method has the potential to reduce the error of the drift estimation, thereby improving the accuracy of the model.

Suggested Citation

  • Christian Wiedemann & Matthias Wächter & Joachim Peinke & Jan A. Freund, 2024. "Improved estimation of drift coefficients using optimal local bandwidths," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(4), pages 1-10, April.
    • Handle: RePEc:spr:eurphb:v:97:y:2024:i:4:d:10.1140_epjb_s10051-024-00686-4
    DOI: 10.1140/epjb/s10051-024-00686-4
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    References listed on IDEAS

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    1. Isaias H. Salgado-Ugarte & Marco A. Perez-Hernandez, 2003. "Exploring the use of variable bandwidth kernel density estimators," Stata Journal, StataCorp LLC, vol. 3(2), pages 133-147, June.
    2. Cai, Zongwu, 2001. "Weighted Nadaraya-Watson regression estimation," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 307-318, February.
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    Cited by:

    1. Christian Wiedemann & Matthias Wächter & Jan A. Freund & Joachim Peinke, 2025. "Local statistical moments to capture Kramers–Moyal coefficients," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(2), pages 1-13, February.

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