https://doi.org/10.1140/epjb/s10051-024-00686-4
Regular Article - Statistical and Nonlinear Physics
Improved estimation of drift coefficients using optimal local bandwidths
1
Carl von Ossietzky Universität Oldenburg, School of Mathematics and Science, Institute of Physics, 26129, Oldenburg, Germany
2
ForWind - Center for Wind Energy Research, Küpkersweg 70, 26129, Oldenburg, Germany
3
ICBM - Institute for Chemistry and Biology of the Marine Environment, Carl-von-Ossietzky-Straße 9-11, 26129, Oldenburg, Germany
a
christian.wiedemann@uni-oldenburg.de
Received:
21
December
2023
Accepted:
4
April
2024
Published online:
24
April
2024
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.
© The Author(s) 2024
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