We propose a vector auto-regressive model with a low-rank constraint on the transition matrix. This model is well suited to predict high-dimensional series that are highly correlated, or that are driven by a small number of hidden factors. While our model has formal similarities with factor models, its structure is more a way to reduce the dimension in order to improve the predictions, rather than a way to define interpretable factors. We provide an estimator for the transition matrix in a very general setting and study its performances in terms of prediction and adaptation to the unknown rank. Our method obtains good result on simulated data, in particular when the rank of the underlying process is small. On macroeconomic data from Giannone et al. (Rev Econ Stat 97(2):436–451, 2015), our method is competitive with state-of-the-art methods in small dimension and even improves on them in high dimension.

中文翻译：

---

具有低秩过渡的高维VAR

我们提出了一种对转移矩阵具有低秩约束的向量自回归模型。该模型非常适合预测高度相关或由少量隐藏因素驱动的高维序列。尽管我们的模型与因子模型在形式上有相似之处，但其结构更多是减小维数以改进预测的方法，而不是定义可解释因子的方法。我们在一个非常笼统的环境中为过渡矩阵提供了一个估计器，并根据预测和适应未知等级来研究其性能。我们的方法在模拟数据上获得了良好的结果，尤其是当基础流程的等级较小时。关于Giannone等人的宏观经济数据。（2015年修订版《经济统计》第97（2）：436–451条），