Robust Covariance Matrix Estimator with Change Points for Multivariate Jump Diffusion Process

We propose a method for constructing covariance matrix estimators robust to abrupt and persistent changes in the underlying spot covariance of a multivariate jump-diffusion process. We take the consistent estimator of the increments of the integrated covariance process and rebuild them as a group of co-occurring signals. We then construct ĝ.,"1-regularized versions using the group LASSO method to detect co-occurring changes in these signals. The group LASSO method is computationally efficient and uses reduced dynamic programming to eliminate spurious change points. The algorithm is computationally fast and accurately identifies the structural common change points in the underlying integrated covariance matrix increments. We empirically demonstrate that the proposed estimator outperforms the benchmark estimators in various forecasting metrics, using different training windows and data frequencies.