Statistical Inference for Unified Garch–Itô Models with High‐Frequency Financial Data
针对统一GARCH-Itô模型，提出一种基于高频金融数据的有限观测期参数估计方法，通过拟似然函数和已实现波动率估计参数，并建立渐近理论，适用于股票价格数据分析。
The existing estimation methods for the model parameters of the unified GARCH–Itô model (Kim and Wang, ) require long period observations to obtain the consistency. However, in practice, it is hard to believe that the structure of a stock price is stable during such a long period. In this article, we introduce an estimation method for the model parameters based on the high‐frequency financial data with a finite observation period. In particular, we establish a quasi‐likelihood function for daily integrated volatilities, and realized volatility estimators are adopted to estimate the integrated volatilities. The model parameters are estimated by maximizing the quasi‐likelihood function. We establish asymptotic theories for the proposed estimator. A simulation study is conducted to check the finite sample performance of the proposed estimator. We apply the proposed estimation approach to the Bank of America stock price data.