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A class of optimal tests for contemporaneous non-causality in VAR models

机译：VAR模型中同时存在非因果关系的一类最优检验

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摘要

The aim of this paper was to test for contemporaneous non-causality defined by Granger (1969) between two groups of variables in a VAR(p) setting. Since contemporaneous correlation of the innovations is a necessary condition for contemporaneous causality (Pierce and Haugh, 1977), we focused on testing some restrictions on the covariance matrix of the noise. The class of the derived tests is locally asymptotically most stringent (in the Le Cam sense), invariant with respect to the group of block affine transformations and asymptotically invariant with respect to the group of continuous monotone radial transformations. Those tests are based on multivariate ranks of distances and multivariate signs of the o bservations and are shown to be asymptotically distribution free under very mild assumptions on the noise.
机译：本文的目的是测试在VAR（p）设置下两组变量之间由Granger（1969）定义的同期非因果关系。由于创新的同期相关性是同期因果关系的必要条件（Pierce和Haugh，1977），因此我们集中于测试对噪声协方差矩阵的一些限制。派生测试的类别在局部渐近性上最严格（在Le Cam意义上），相对于块仿射变换组是不变的，而对于连续单调径向变换则是渐近不变的。这些测试基于距离的多元等级和观测的多元符号，并在非常温和的噪声假设下被证明是渐近分布的。

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