论文标题
高维矢量自回归模型的统计估计
Statistical Estimation of High-Dimensional Vector Autoregressive Models
论文作者
论文摘要
高维矢量自回旋（VAR）模型是用于分析多元时间序列的重要工具。本文着重于高维时间序列以及针对将稀疏VAR模型拟合到该时间序列的不同正规估计程序。注意对VAR参数施加的不同稀疏假设以及这些稀疏性假设与建立的估计器的特定一致性属性如何相关。提出了针对高维var模型的稀疏方案，该模型被认为更适合考虑的时间序列设置。此外，据表明，在这种稀疏设置下，将持有的持有范围扩大了正则化估计器的一致性属性到广泛的矩阵规范。除其他事项外，此功能可以将VAR参数估计器应用于不同的推理问题，例如预测或估算基础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规估计量的有限样本行为。
High-dimensional vector autoregressive (VAR) models are important tools for the analysis of multivariate time series. This paper 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 considered. Furthermore, it is shown that, under this sparsity setting, threholding extents 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 inference 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.
