A Geometric Approach for Forecasting Realized Covariances

In this study, we propose a novel approach for forecasting realized covariance (RCOV) matrices of asset returns using a Riemannian-geometry-aware deep learning framework. In this way, we account for the geometric properties of covariance matrices, naturally handling the symmetric positive-definite constraint while considering non-linear dynamics, and efficiently managing high-dimensionality. Moreover, by using the Fréchet sample mean of RCOV matrices, we extend the heterogeneous autoregressive model to a geometric approach in the matrix-variate framework. We apply our approach to forecast daily RCOV matrices for fifty among the most capitalized companies in the S&P 500 index and show that the methods presented in this study outperform traditional approaches in terms of predictive accuracy.