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，参数维数会急剧膨胀。因此，秩约简建模具有吸引力且已得到充分发展。但在几乎所有应用中，拟合模型的稳定性是一项基本要求，而这一要求在秩约简情形下尚未得到解决。本文首次推导出一种闭式解形式的秩约简转移矩阵估计量，该估计量能够保证稳定性。我们证明该估计量具有一致性和渐近统计有效性，并通过对比仿真验证其性能。