Threshold estimation for jump-diffusions under small noise asymptotics

TL;DR

This paper develops a new threshold-based quasi-likelihood estimator for jump-diffusion models with small noise, proving its consistency and asymptotic normality, and introduces a novel localization technique to handle diverse jumps.

Contribution

It introduces a new localization argument that eliminates the need for truncation, allowing for broader jump classes in threshold estimation of jump-diffusions.

Findings

Estimator is consistent and asymptotically normal.

New localization method simplifies the contrast function.

Applicable to a wider class of jumps than previous methods.

Abstract

We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and asymptotic normality under new asymptotics. One of the novelties of the paper is that we give a new localization argument, which enables us to avoid truncation in the contrast function that has been used in earlier works and to deal with a wider class of jumps in threshold estimation than ever before.