Cross-Correlation Matrices for Tests of Independence and Causality Between Two Multivariate Time Series
用于检验两组多变量时间序列独立性与因果关系的交叉相关矩阵AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确研究两组多变量时间序列的独立性、交叉相关结构与方向性检验，最直接对应时间序列方向。
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用于检验两组多变量时间序列独立性与因果关系的交叉相关矩阵
- 研究问题
- 研究两组可能为多变量的时间序列如何检验独立性，以及如何借助交叉相关结构判断序列间因果关系的位置与方向。
- 方法与思路
- 作者构造块 Toeplitz 矩阵，以矩阵平方的迹和行列式构造检验统计量，并提出探查序列间因果位置或方向的矩阵检验。
- 材料陈述的贡献
- 摘要称，对数行列式检验比原假设下渐近等价的其他检验更有力，模拟也显示相对既有方法的改进。
- 阅读关注点
- 阅读时应核对矩阵的滞后构造、统计量的零假设分布、功效比较适用条件，以及因果方向检验的具体定义。
- 阅读边界
- 摘要未说明功效优势的完整条件及模拟设计；所称因果方向不能直接解读为经济干预效应，仍须核对全文定义。
原文摘要
An often-studied problem in time series analysis is that of testing for the independence of two (potentially multivariate) time series. Toeplitz matrices have demonstrated utility for the related setting of time series goodness-of-fit testing—ergo, herein, we extend those concepts by defining a nontrivial block Toeplitz matrix for use in the setting of independence testing. We propose test statistics based on the trace of the square of the matrix and determinant of the matrix; these statistics are connected to one another as well as known statistics previously proposed in the literature. Furthermore, the log of the determinant is argued to relate to a likelihood ratio test and is proven to be more powerful than other tests that are asymptotically equivalent under the null hypothesis. Additionally, matrix-based tests are presented for the purpose of inferring the location or direction of the causality existing between the two series. A simulation study is provided to explore the efficacy of the proposed methodology—the methods are shown to offer improvement over existing techniques, which include the famous Granger causality test. Finally, data examples involving U.S. inflation, trade volume, and exchange rates are given. Supplementary materials for this article are available online.