Stable Reduced-Rank VAR Estimators in Closed Forms

The vector autoregression (VAR) is widely used to model dynamical systems. As the model dimension increases, the reduced-rank (RR) VAR modelling effectively reduces the number of parameters significantly by factorization and mitigates the risk of overfitting. However, the crucial problem in identification is to guarantee the estimated system is stable. Here, we develop a category of stable, closed-form, consistent RR-VAR estimators based on correlation. In numerical illustrations, we compare our new RR correlation stable estimators with our previous RR stable estimators based on the forwards-backwards optimization.