  The vector autoregression (VAR) has been widely used in system
identification, econometrics, natural science, and many other areas. However,
when the state dimension becomes large the parameter dimension explodes. So
rank reduced modelling is attractive and is well developed. But a fundamental
requirement in almost all applications is stability of the fitted model. And
this has not been addressed in the rank reduced case. Here, we develop, for the
first time, a closed-form formula for an estimator of a rank reduced transition
matrix which is guaranteed to be stable. We show that our estimator is
consistent and asymptotically statistically efficient and illustrate it in
comparative simulations.
