Unified discrete-time factor stochastic volatility and continuous-time Itô models for combining inference based on low-frequency and high-frequency

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