Fitting Vast Dimensional Time-Varying Covariance Models

Estimation of time-varying covariances is a key input in risk management and asset allocation. ARCH-type multivariate models are used widely for this purpose. Estimation of such models is computationally costly and parameter estimates are meaningfully biased when applied to a moderately large number of assets. Here, we propose a novel estimation approach that suffers from neither of these issues, even when the number of assets is in the hundreds. The theory of this new method is developed in some detail. The performance of the proposed method is investigated using extensive simulation studies and empirical examples. Supplementary materials for this article are available online.