A latent dynamic factor approach to forecasting multivariate stock market volatility

This paper proposes a latent dynamic factor model for low- as well as high-dimensional realized covariance matrices of stock returns. The approach is based on the matrix logarithm and allows for flexible dynamic dependence patterns by combining common latent factors driven by HAR dynamics and idiosyncratic AR(1) factors. The model accounts for symmetry and positive definiteness of covariance matrices without imposing parametric restrictions. Simulated Bayesian parameter estimates as well as positive definite (co)variance forecasts are obtained using Markov Chain Monte Carlo (MCMC) methods. An empirical application to 5-dimensional and 30-dimensional realized covariance matrices of daily New York Stock Exchange (NYSE) stock returns shows that the model outperforms other approaches of the extant literature both in-sample and out-of-sample.