Abstract

This paper proposes a simple approach for forecasting large dimensional covariance matrices with the help of a latent factor structure with stochastic volatility components applied to realized covariance matrices. The factor structure together with the conditional Wishart distribution automatically assures positive-definiteness, symmetry and thick-tails, captures the commonality in the dynamics and the long-persistence of the autocorrelation of realized (co)variances within a unified parsimonious
framework with no parameter constraints. The Factor Autoregressive model we propose profits from what alternatives suffer, namely the curse of dimensionality: higher the matrix dimension, higher the efficiency of the estimates and forecasts. The model has a non-Gaussian non-linear state-space representation that we estimate by maximum likelihood together with a non-Gaussian filtering technique. Monte Carlo simulations provide evidence for the accuracy of the estimates and the comprehensive empirical application to DJIA components proves the usefulness of the model to accurately forecast large dimensional covariance matrices.