  We provide a novel method for large volatility matrix prediction with
high-frequency data by applying eigen-decomposition to daily realized
volatility matrix estimators and capturing eigenvalue dynamics with ARMA
models. Given a sequence of daily volatility matrix estimators, we compute the
aggregated eigenvectors and obtain the corresponding eigenvalues. Eigenvalues
in the same relative magnitude form a time series and the ARMA models are
further employed to model the dynamics within each eigenvalue time series to
produce a predictor. We predict future large volatility matrix based on the
predicted eigenvalues and the aggregated eigenvectors, and demonstrate the
advantages of the proposed method in volatility prediction and portfolio
allocation problems.
