Anderson Brian D O, Deistler Manfred, Dufour Jean-Marie
School of Automation Hangzhou Dianzi University Hangzhou China.
Research School of Engineering, ANU College of Engineering and Computer Science Australian National University Acton Australia.
J Time Ser Anal. 2019 Jan;40(1):102-123. doi: 10.1111/jtsa.12430. Epub 2018 Sep 23.
This article studies the sensitivity of Granger causality to the addition of noise, the introduction of subsampling, and the application of causal invertible filters to weakly stationary processes. Using canonical spectral factors and Wold decompositions, we give general conditions under which additive noise or filtering distorts Granger-causal properties by inducing (spurious) Granger causality, as well as conditions under which it does not. For the errors-in-variables case, we give a continuity result, which implies that: a 'small' noise-to-signal ratio entails 'small' distortions in Granger causality. On filtering, we give general necessary and sufficient conditions under which 'spurious' causal relations between (vector) time series are not induced by linear transformations of the variables involved. This also yields transformations (or filters) which can eliminate Granger causality from one vector to another one. In a number of cases, we clarify results in the existing literature, with a number of calculations streamlining some existing approaches.
本文研究了格兰杰因果关系对噪声添加、子采样引入以及因果可逆滤波器应用于弱平稳过程的敏感性。利用规范谱因子和沃尔德分解，我们给出了加性噪声或滤波通过诱导（虚假）格兰杰因果关系扭曲格兰杰因果属性的一般条件，以及不产生这种情况的条件。对于变量误差情况，我们给出了一个连续性结果，这意味着：“小”的噪声与信号比会导致格兰杰因果关系中的“小”扭曲。关于滤波，我们给出了一般的充要条件，在这些条件下，（向量）时间序列之间的“虚假”因果关系不会由所涉及变量的线性变换诱导产生。这也产生了可以消除从一个向量到另一个向量的格兰杰因果关系的变换（或滤波器）。在许多情况下，我们澄清了现有文献中的结果，通过一些计算简化了一些现有方法。
