Dynamic Covariance Estimation under Structural Assumptions via a Joint Optimization Approach

Dynamic covariance estimation is a problem of fundamental importance in statistics, econometrics, with important applications in finance, especially portfolio optimization. While there is a large body of work on static covariance estimation, the current literature on dynamic covariance estimation is somewhat limited in comparison. We propose a flexible optimization framework to simultaneously learn covariance matrices across different time periods under suitable structural assumptions on the period-specific covariance matrices and time-varying regularizers. We propose a novel efficient joint optimization algorithm to learn the covariance matrices simultaneously. Our numerical experiments demonstrate the computation improvements of our algorithm over both off-the-shelf solvers and other dynamic covariance estimation methods. We also see notable gains in terms of test MSE and downstream portfolio optimization tasks on both synthetic and real datasets.