Dynamic Covariance Models

Recent efforts have focused on modeling static covariance matrices where pairwise covariances are considered invariant. In many real systems, however, these pairwise relations often change.

To characterize the changing correlations in a high-dimensional system, we study a class of dynamic covariance models (DCMs) assumed to be sparse, and investigate for the first time a unified theory for understanding their nonasymptotic error rates and model selection properties. In particular, in the challenging high-dimensional regime, we highlight a new uniform consistency theory in which the sample size can be seen as n 4/5 when the bandwidth parameter is chosen as h ∝ n − 1/5 for accounting for the dynamics.