Estimation of ergodic square-root diffusion under high-frequency sampling

TL;DR

This paper develops a practical two-stage Gaussian quasi-likelihood estimation method for the ergodic square-root diffusion process using high-frequency data, achieving asymptotic efficiency and high-precision parameter estimates.

Contribution

It introduces a simple, two-stage estimation procedure that leverages high-frequency sampling to improve efficiency and precision in estimating the parameters of the square-root diffusion process.

Findings

Asymptotic covariance matrix simplifies under high-frequency sampling.

The proposed method achieves asymptotic efficiency.

Simulation results confirm high-precision estimation.

Abstract

Gaussian quasi-likelihood estimation of the parameter $\theta$ in the square-root diffusion process is studied under high frequency sampling. Different from the previous study of Overbeck and Ryd\'{e}n(1998) under low-frequency sampling, high-frequency of data provides very simple form of the asymptotic covariance matrix. Through easy-to-compute preliminary contrast functions, a practical two-stage manner without numerical optimization is formulated in order to conduct not only an asymptotically efficient estimation of the drift parameters, but also high-precision estimator of the diffusion parameter. Simulation experiments are given to illustrate the results.