Parsimonious modeling of high-dimensional realized correlation matrices via compression and shrinkage

A forecast for a correlation matrix is pivotal for many financial applications. This thesis proposes to model and forecast realized correlations by a parsimonious factor framework, where the dynamics are driven by time-varying factors. By adapting non-linear shrinkage procedures developed by Ledoit and Wolf (2020), shrunken eigenvalues are taken as estimators for factors. We applied our modeling approach to a 50-dimension time series of realized correlation matrices. We document forecast improvements based on both statistical and economical loss functions as compared to the benchmark models both in-sample and out-ofsample. Our results show that modeling with small numbers of factors suffices. In addition, the controled and empirical studies show that our modeling with the shrunken eigenvalues performs better than that with the sample eigenvalues.