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

We study the Gaussian quasi-likelihood estimation of the parameter $\theta:=(\alpha,\beta,\gamma)$ of the square-root diffusion process, also known as the Cox-Ingersoll-Ross (CIR) model, observed at high frequency. Different from the previous study [1] under low-frequency sampling, high-frequency of data provides us with very simple form of the asymptotic covariance matrix. Through easy-to-compute preliminary contrast functions, we formulate a practical two-stage manner without numerical optimization 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. [1] L. Overbeck and T. Ryd\'en. Estimation in the Cox-Ingersoll-Ross model. Econometric Theory, 13(3): 430-461, 1997.