This article aims to decompose a large dimensional vector autoregressive (VAR) model into two components, the first one being generated by a small-scale VAR and the second one being a white noise. Hence, a reduced number of common components generates the entire dynamics of the large system through a VAR structure. This modelling, which we label as the dimension-reducible VAR, extends the common feature approach to high-dimensional systems, and it differs from the dynamic factor model in which the idiosyncratic component can also embed a dynamic pattern. We show the conditions under which this decomposition exists. We provide statistical tools to detect its presence in the data and to estimate the parameters of the underlying small-scale VAR model. Based on our methodology, we propose a novel approach to identify the shock that is responsible for most of the common variability at the business cycle frequencies. We evaluate the practical value of the proposed methods by simulations as well as by an empirical application to a large set of US economic variables.

中文翻译：

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高维向量自回归模型的降维*

本文旨在将大维向量自回归 (VAR) 模型分解为两个分量，第一个由小规模 VAR 生成，第二个由白噪声生成。因此，减少数量的公共组件通过 VAR 结构生成了大型系统的整个动态。这种建模，我们将其标记为可降维的 VAR，将通用特征方法扩展到高维系统，它不同于动态因子模型，其中特殊组件也可以嵌入动态模式。我们展示了这种分解存在的条件。我们提供统计工具来检测它在数据中的存在并估计底层小规模 VAR 模型的参数。根据我们的方法，我们提出了一种新的方法来识别造成商业周期频率中大多数常见变化的冲击。我们通过模拟以及对大量美国经济变量的经验应用来评估所提出方法的实用价值。