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This paper introduces unified models for high-dimensional factor-based Itoprocess, which can accommodate both continuous-time Ito diffusion anddiscrete-time stochastic volatility (SV) models by embedding the discrete SVmodel in the continuous instantaneous factor volatility process. We call it theSV-Ito model. Based on the series of daily integrated factor volatility matrixestimators, we propose quasi-maximum likelihood and least squares estimationmethods. Their asymptotic properties are established. We apply the proposedmethod to predict future vast volatility matrix whose asymptotic behaviors arestudied. A simulation study is conducted to check the finite sample performanceof the proposed estimation and prediction method. An empirical analysis iscarried out to demonstrate the advantage of the SV-Ito model in volatilityprediction and portfolio allocation problems.

Unified Discrete-Time Factor Stochastic Volatility and Continuous-Time Ito Models for Combining Inference Based on Low-Frequency and High-Frequency