High-dimensional-20 vector autoregressive (VAR) models are important tools for the analysis of multi-variate time series. This article focuses on high-dimensional time series and on the different regularized estimation procedures proposed for fitting sparse VAR models to such time series. Attention is paid to the different sparsity assumptions imposed on the VAR parameters and how these sparsity assumptions are related to the particular consistency properties of the estimators established. A sparsity scheme for high-dimensional VAR models is proposed which is found to be more appropriate for the time series setting. Furthermore, it is shown that, under this sparsity setting, thresholding extends the consistency properties of regularized estimators to a wide range of matrix norms. Among other things, this enables application of the VAR parameters estimators to different problems, like forecasting or estimating the second-order characteristics of the underlying VAR process. Extensive simulations compare the finite sample behavior of the different regularized estimators proposed using a variety of performance criteria.

中文翻译：

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高维向量自回归模型的稀疏性概念和估计程序

高维 20 向量自回归 (VAR) 模型是分析多变量时间序列的重要工具。本文重点介绍高维时间序列以及为将稀疏 VAR 模型拟合到此类时间序列而提出的不同正则化估计程序。注意施加在 VAR 参数上的不同稀疏假设以及这些稀疏假设如何与建立的估计量的特定一致性属性相关。提出了一种用于高维 VAR 模型的稀疏方案，发现它更适合时间序列设置。此外，研究表明，在这种稀疏设置下，阈值化将正则化估计量的一致性属性扩展到广泛的矩阵范数。除其他事项外，这使得 VAR 参数估计器能够应用于不同的问题，例如预测或估计基础 VAR 过程的二阶特征。广泛的模拟比较了使用各种性能标准提出的不同正则化估计器的有限样本行为。