Update estimation of diffusion parameter observed at high frequency

TL;DR

This paper introduces an updated estimation method for diffusion parameters using high-frequency data, ensuring asymptotic properties similar to quasi-MLE, with validation through simulation.

Contribution

It presents a novel update estimation technique for diffusion parameters that maintains asymptotic normality and efficiency in the presence of nuisance drift.

Findings

Estimator is asymptotically equivalent to quasi-MLE

Estimator achieves asymptotic normality

Simulation confirms theoretical properties

Abstract

We propose an update estimation method for a diffusion parameter from high-frequency dependent data under a nuisance drift element. We ensure the asymptotic equivalence of the estimator to the corresponding quasi-MLE, which has the asymptotic normality and the asymptotic efficiency. We give a simulation example to illustrate the theory.