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.

翻译：向量自回归(VAR)已在系统辨识、计量经济学、自然科学及众多其他领域得到广泛应用。然而，当状态维数增大时，参数维数会随之激增。因此，降秩建模具有吸引力且已发展成熟。但在几乎所有应用中，拟合模型的稳定性都是一个基本要求，而这一要求在降秩情形下尚未得到解决。本文首次提出了一种确保稳定的降秩转移矩阵估计量的闭合表达式。我们证明了该估计量具有一致性和渐近统计有效性，并通过对比仿真实验对其进行了验证。