Forecasting Large Realized Covariance Matrices: The Benefits of Factor Models and Shrinkage

Abstract We propose a model to forecast large realized covariance matrices of returns, applying it the constituents S&P 500 daily. To address curse dimensionality, we decompose return matrix using standard firm-level factors (e.g., size, value, and profitability) use sectoral restrictions in residual matrix. This restricted is then estimated vector heterogeneous autoregressive models with least absolute shrinkage selection operator. Our methodology improves forecasting precision relative benchmarks leads better estimates minimum variance portfolios.