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

Abstract

Gaussian quasi-likelihood estimation of the parameter in the square-root diffusion process is studied under high-frequency sampling. Different from previous studies under low-frequency sampling, high-frequency of data leads to a 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 to conduct not only an asymptotically efficient estimation of the drift parameters but also a high-precision estimator of the diffusion parameter. Simulation experiments are given to illustrate the results.