Symmetric VAR(1) Modelling with Guaranteed Stability

Abstract

The first order vector autoregression with a symmetric transition matrix (sym-VAR(1)) occurs widely in applications such as electrical networks, robotics and mechanical systems. However, there is so far almost no work on estimating a sym- VAR(1) from time series data that guarantees the estimated system matrix is Schur stable. Here, we develop, for the first time, a closed-form estimator that guarantees symmetry and stability.