Abstract: This paper introduces a novel multivariate GARCH-Itô model that integrates the structural framework of multivariate GARCH within a continuous-time diffusion process, providing a unified approach to modeling the dynamic evolution of volatility matrices by jointly utilizing high-frequency and low-frequency data. We develop a quasi-maximum likelihood estimation method for parameter inference and establish the corresponding asymptotic theory. To address the challenges associated with high-dimensional asset spaces, the proposed model is coupled with a factor structure, enabling scalable and efficient prediction of large integrated volatility matrices. Theoretical guarantees for the proposed predictor are provided under high-dimensional settings. Extensive simulation studies are conducted to examine the finite-sample performance of both the estimation and prediction procedures across both low-dimensional and high-dimensional contexts. In an empirical application, we analyze 270 constituent stocks of the CSI 300 index using minute-level high-frequency data from January 1, 2018, to December 31, 2020. The results demonstrate that the multivariate GARCH-Itô model consistently outperforms several benchmark methods in terms of integrated volatility matrix forecasting and portfolio allocation, offering a flexible and unified framework that incorporates both high- and low-frequency data features for advanced volatility modeling and prediction.

Key words: High-frequency data, Dynamic structure, Quisi-maximum likelihood method, Integrated volatility matrix, Factor model.