Contrast estimation of the Vasicek integrated diffusion process for high-frequency data

Abstract

The purpose of this paper is to study the parameter estimation of the Vasicek integrated diffusion process. Based on the contrast function, the parameter contrast estimators of the Vasicek integrated diffusion process are given, and the mean-square errors of drift parameter estimators are derived, so as to obtain the optimal sampling intervals for the parameter estimators. Then we prove the strong consistency of the contrast estimators by the tail probability exponential inequality of α-mixing long-span high-frequency data. In numerical simulation, we investigate the fitting effect of the estimates under different sampling intervals and different sample sizes. The results indicate that using optimal interval sampling can achieve good estimation performance. We use the daily closing price data of CSI 300 index to conduct an empirical analysis and give a logarithmic price prediction model. The analysis results show that the prediction model works well.