Parameter estimation for Vasicek model driven by a general Gaussian noise

TL;DR

This paper develops estimators for the Vasicek model driven by general Gaussian noise, proving their consistency and asymptotic normality, extending previous results to broader noise types.

Contribution

It introduces new estimation methods for the Vasicek model with general Gaussian noise and proves their statistical properties, extending prior work to more general noise processes.

Findings

Constructed least squares and moment estimators.

Proved consistency and asymptotic normality of estimators.

Extended previous results to general Gaussian noise.

Abstract

This paper developed an inference problem for Vasicek model driven by a general Gaussian process. We construct a least squares estimator and a moment estimator for the drift parameters of the Vasicek model, and we prove the consistency and the asymptotic normality. Our approach extended the result of Xiao and Yu (2018) for the case when noise is a fractional Brownian motion with Hurst parameter H \in [1/2,1).