A latent dynamic factor approach to forecasting multivariate stock market volatility

This paper proposes a latent dynamic factor model for high-dimensional realized covariance matrices of stock returns. The approach is based on the matrix logarithm and combines common latent factors driven by HAR processes and idiosyncratic autoregressive dynamics. The model accounts for positive definiteness of covariance matrices without imposing parametric restrictions. Simulated Bayesian parameter estimates are obtained using basic Markov chain Monte Carlo methods. An empirical application to 5-dimensional and 30-dimensional realized covariance matrices shows remarkably good forecasting results, in-sample and out-of-sample.