Improved estimation of drift coefficients using optimal local bandwidths

Christian Wiedemann (), Matthias Wächter, Joachim Peinke and Jan A. Freund
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Christian Wiedemann: School of Mathematics and Science, Institute of Physics
Matthias Wächter: School of Mathematics and Science, Institute of Physics
Joachim Peinke: School of Mathematics and Science, Institute of Physics
Jan A. Freund: School of Mathematics and Science, Institute of Physics

The European Physical Journal B: Condensed Matter and Complex Systems, 2024, vol. 97, issue 4, 1-10

Abstract: 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.

Date: 2024
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DOI: 10.1140/epjb/s10051-024-00686-4

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