The Nadaraya–Watson estimation of uncertain differential equations with applications in financial market

This paper proposes a nonparametric Nadaraya–Watson estimator for the drift and diffusion terms in homogeneous uncertain differential equations with unknown structures. We validate its performance using two numerical examples with residual analysis and an empirical study on the Dow Jones Americas Basic Materials Index. Compared to existing methods, our estimator is more robust to outliers and requires no prior knowledge of the drift or diffusion term structures.