High-dimensional covariance forecasting based on principal component analysis of high-frequency data

This study provides a new approach to forecasting high-dimensional covariance matrices based on a principal component analysis (PCA) of high-frequency data, by which realized eigenvalues could be estimated and modeled. Our method can avoid the so-called "curse of dimensionality" and handle the case that the number of assets is time-varying. In particular, we propose four (V)HAR-type dynamic models for predicting high-dimensional covariance matrices. All of them can well characterize the long memory behavior of realized eigenvalue series and be easily estimated by OLS. The empirical evidence shows that they outperform the competing models without consideration of long memory behavior in terms of in-sample fitting, out-of-sample prediction, and out-of-sample portfolio allocation.