论文标题
高维稀疏矢量自动化中参数的置信区间
Confidence intervals for parameters in high-dimensional sparse vector autoregression
论文作者
论文摘要
矢量自动进度（VAR）模型被广泛用于分析随着时间的推移多个变量之间的相互关系。 VAR模型过渡矩阵的估计和推断对于从业者在经济学和金融等领域做出决策至关重要。但是，当变量的数量大于样本量时，执行模型参数的统计推断仍然是一个挑战。在本文中，我们提出了偏低的拉索和两个引导性脱偏的套索方法，以构建高维var模型过渡矩阵元素的置信区间。我们表明，在适当的稀疏性和其他规律性条件下，提出的方法在渐近上有效。为了实现我们的方法，我们开发了可行且可行的可行算法，从而节省了NodeWise Lasso和Bootstrap所需的大量计算。一项仿真研究表明，我们的方法在有限样品中的表现良好。最后，我们采用方法来分析2019年标准普尔500指数中股票的价格数据。我们发现，一些股票（例如世界上最大的黄金生产商，纽蒙特公司）具有对大多数股票的显着预测能力。
Vector autoregression (VAR) models are widely used to analyze the interrelationship between multiple variables over time. Estimation and inference for the transition matrices of VAR models are crucial for practitioners to make decisions in fields such as economics and finance. However, when the number of variables is larger than the sample size, it remains a challenge to perform statistical inference of the model parameters. In this article, we propose the de-biased Lasso and two bootstrap de-biased Lasso methods to construct confidence intervals for the elements of the transition matrices of high-dimensional VAR models. We show that the proposed methods are asymptotically valid under appropriate sparsity and other regularity conditions. To implement our methods, we develop feasible and parallelizable algorithms, which save a large amount of computation required by the nodewise Lasso and bootstrap. A simulation study illustrates that our methods perform well in finite samples. Finally, we apply our methods to analyze the price data of stocks in the S&P 500 index in 2019. We find that some stocks, such as the largest producer of gold in the world, Newmont Corporation, have significant predictive power over the most stocks.
