Nonparametric Estimation for Jump-Diffusion CIR Model

TL;DR

This paper develops a nonparametric estimation method for the jump intensity in a jump-diffusion CIR model using low frequency data, proving its consistency and asymptotic properties.

Contribution

It introduces a novel nonparametric estimator for jump intensity in the jump-diffusion CIR model, with theoretical guarantees.

Findings

Estimator is measurable and consistent

Asymptotic risk bounds are derived

Method performs well with low frequency observations

Abstract

We study the nonparametric estimation for the intensity of Poisson random measure in jump-diffusion CIR model based on the low frequency observations. This is given in terms of the minimization of norms on a nonempty, closed and convex subset of some special Hilbert space. We establish the measurability of the estimator and derive its consistency and asymptotic risk bound.