Model Selection for Diffusion Coefficient Estimation in SDE
Résumé
This paper introduces a projection-based estimator for the diffusion coefficient in a stochastic differential equation (SDE) using high-frequency observations of a single trajectory. The method extends existing approaches to noncompact estimation domains, allowing the use of projection spaces spanned by noncompactly supported functions such as Hermite and Laguerre bases. The improvement partly relies on a different decomposition of the squared increments of the processes, which define the approximate regression equation. We propose a data-driven model selection procedure and prove that it enables the estimator to automatically balance squared bias and variance. Numerical experiments confirm its effectiveness across various SDE settings.