  This paper introduces a unified factor overnight GARCH-It\^o model for large
volatility matrix estimation and prediction. To account for whole-day market
dynamics, the proposed model has two different instantaneous factor volatility
processes for the open-to-close and close-to-open periods, while each embeds
the discrete-time multivariate GARCH model structure. To estimate latent factor
volatility, we assume the low rank plus sparse structure and employ
nonparametric estimation procedures. Then, based on the connection between the
discrete-time model structure and the continuous-time diffusion process, we
propose a weighted least squares estimation procedure with the non-parametric
factor volatility estimator and establish its asymptotic theorems.
