Title: Modelling dynamic covariance matrices with stochastic volatility latent factors
Authors: Roxana Halbleib - University of Konstanz (Germany) [presenting]
Giorgio Calzolari - University of Firenze (Italy)
Abstract: A new method is proposed to model and forecast large dimensional covariance matrices of daily returns by taking advantage of the commonality in their dynamics by means of a latent factor structure with stochastic volatility. As such a model is very difficult to estimate from daily returns, we use the richer information content of intraday returns incorporated in realized covariance matrices, which are consistent estimates of the multivariate daily variation. Our stochastic volatility latent factor model is able to capture the empirical features of daily covariance matrices, such as commonality in dynamics and long persistence in autocorrelation, within a very parsimonious framework: the number of the parameters is of order $O(n)$ compared to the ones of existing multivariate dynamic volatility approaches, which are of order at least $O(n^2)$. The proposed model has a non-Gaussian non-linear state-space representation; we estimate it my means of exact numerical maximum-likelihood using the non-Gaussian filtering approach previously proposed. We prove the accuracy of the parameter estimates within a Monte Carlo study and the usefulness of our approach to forecast high-dimensional covariance matrices within an empirical application to daily realized covariance matrices of the DJIA components.