Estimation of High-Dimensional Volatility Matrices with Dynamic Conditional Correlation-embedded Mixed Factor Structures

Estimating large volatility matrices is essential to finance research in the era of big data. We propose a unified estimate that embeds a dynamic conditional correlation GARCH (DCC-GARCH) structure into a mixed factor model comprising both observable and weak latent factors, with the residual covariance estimated through an adaptively thresholded sparse matrix based on the extended Principal Orthogonal Complement Thresholding (ePOET) framework. The resulting method, termed DCC-ePOET, jointly captures pervasive signals from both types of factors and dynamic idiosyncratic co-volatilities. It resolves the singularity issue that arises in high-dimensional settings where the cross-sectional dimension N exceeds the serial dimension T, while remaining computationally feasible. Monte Carlo simulations confirm the good finite sample performance of DCC-ePOET across various dimensions. An out-of-sample minimum variance portfolio analysis using S&P 500 data demonstrates the usefulness of DCC-ePOET in practice.