Statistical Inference for Unified Garch-Ito Models with High-Frequency Financial Data

Abstract

The existing estimation methods for the model parameters of the unified GARCH-Ito 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.