一种多元非线性因果关系的新测试。
A new test of multivariate nonlinear causality.
作者信息
Bai Zhidong, Hui Yongchang, Jiang Dandan, Lv Zhihui, Wong Wing-Keung, Zheng Shurong
机构信息
KLASMOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, China.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China.
出版信息
PLoS One. 2018 Jan 5;13(1):e0185155. doi: 10.1371/journal.pone.0185155. eCollection 2018.
The multivariate nonlinear Granger causality developed by Bai et al. (2010) (Mathematics and Computers in simulation. 2010; 81: 5-17) plays an important role in detecting the dynamic interrelationships between two groups of variables. Following the idea of Hiemstra-Jones (HJ) test proposed by Hiemstra and Jones (1994) (Journal of Finance. 1994; 49(5): 1639-1664), they attempt to establish a central limit theorem (CLT) of their test statistic by applying the asymptotical property of multivariate U-statistic. However, Bai et al. (2016) (2016; arXiv: 1701.03992) revisit the HJ test and find that the test statistic given by HJ is NOT a function of U-statistics which implies that the CLT neither proposed by Hiemstra and Jones (1994) nor the one extended by Bai et al. (2010) is valid for statistical inference. In this paper, we re-estimate the probabilities and reestablish the CLT of the new test statistic. Numerical simulation shows that our new estimates are consistent and our new test performs decent size and power.
Bai等人（2010年）（《数学与计算机模拟》。2010年；81：5 - 17）提出的多元非线性格兰杰因果关系在检测两组变量之间的动态相互关系中起着重要作用。遵循Hiemstra和Jones（1994年）（《金融杂志》。1994年；49(5)：1639 - 1664）提出的Hiemstra - Jones（HJ）检验的思路，他们试图通过应用多元U统计量的渐近性质来建立其检验统计量的中心极限定理（CLT）。然而，Bai等人（2016年）（2016年；arXiv: 1701.03992）重新审视了HJ检验，发现HJ给出的检验统计量不是U统计量的函数，这意味着Hiemstra和Jones（1994年）提出的CLT以及Bai等人（2010年）扩展的CLT都不适用于统计推断。在本文中，我们重新估计了概率并重新建立了新检验统计量的CLT。数值模拟表明，我们的新估计是一致的，并且我们的新检验在规模和功效方面表现良好。
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