One-step Local M-estimator for Integrated Jump-Diffusion Models

Abstract

In this paper, robust nonparametric estimators, instead of local linear estimators, are adapted for infinitesimal coefficients associated with integrated jump-diffusion models to avoid the impact of outliers on accuracy. Furthermore, consider the complexity of iteration of the solution for local M-estimator, we propose the one-step local M-estimators to release the computation burden. Under appropriate regularity conditions, we prove that one-step local M-estimators and the fully iterative M-estimators have the same performance in consistency and asymptotic normality. Through simulation, our method present advantages in bias reduction, robustness and reducing computation cost. In addition, the estimators are illustrated empirically through stock index under different sampling frequency.