Abstract
In this research, we explore the estimation of large time-varying correlation matrices. Efficient estimation of time-varying correlation matrices is important in numerous applications, including the analysis of volatility spillovers in unstable economies or the evolution of networks, as well as dynamic portfolio allocation. However, the requirement of a unit diagonal, appropriately bounded off-diagonal entries and positive definiteness provide numerous econometric challenges. Furthermore, the ever-increasing dimensionality of prospective datasets adds yet another layer of complexity. Aiming to address these challenges, we propose to estimate time-varying Pearson correlation matrices through a sequence of time-varying partial correlations with score-driven updating mechanics. Reconstructing the Pearson correlation matrix from the partial correlations ensures all of the aforementioned properties without having to constrain the partial correlations. As an additional benefit, the partial correlations are likely to be sparse in many applications. For example, stock returns may become uncorrelated after removing their correlation with the market. We exploit this sparsity via regularization and demonstrate improvements in finite-sample performance in a Monte Carlo analysis. An application of our estimator to a portfolio of US stocks reveals sparsity patterns that provide novel insights into the financial market structure that may help shed light on the importance of accounting for time-varying correlations, as opposed to solely modelling volatility dynamics.