Comparing unconstrained parametrization methods for return covariance matrix prediction

Forecasting covariance matrices is a difficult task in many research fields since the predicted matrices should be at least positive semidefinite. This problem can be overcome by including constraints in the predictive model or through a parametrization of the matrices to be predicted. In this paper, we focus on the latter approach in a financial application and analyse four parametrizations of the covariance matrices of asset returns. The aim of the manuscript is to understand if the parametrizations of the covariance matrices exhibit differences in terms of predictive accuracy. To this end, we critically analyse their predictive performance through both a Monte Carlo simulation and an empirical application with daily and weekly realized covariance matrices of stock assets. Our findings highlight that the Cholesky decomposition and the parametrization recently introduced by Archakov and Hansen are the overall best-performing methods in terms of forecasting accuracy.