Improved estimation of drift coefficients using optimal local bandwidths

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.