A new test of multivariate nonlinear causality

Zhidong Bai; Yongchang Hui; Dandan Jiang; Zhihui Lv; Wing-Keung Wong; Shurong Zheng

doi:10.1371/journal.pone.0185155

A new test of multivariate nonlinear causality

PLoS One. 2018 Jan 5;13(1):e0185155. doi: 10.1371/journal.pone.0185155. eCollection 2018.

Authors

Zhidong Bai¹, Yongchang Hui², Dandan Jiang³, Zhihui Lv¹, Wing-Keung Wong^{4

5}, Shurong Zheng¹

Affiliations

¹ KLASMOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, China.
² School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China.
³ School of Mathematics, Jilin University, Changchun, China.
⁴ Department of Finance, Asia University, Taichung, Taiwan.
⁵ Department of Economics, Lingnan University, Hong Kong, China.

Abstract

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Causality*
Computer Simulation
Mathematical Concepts
Models, Statistical
Multivariate Analysis*
Nonlinear Dynamics*
Stochastic Processes

Grants and funding

Zhidong Bai’s research was supported by The National Science Foundation of China (11571067 and 11471140). Yongchang Hui’s research was supported by The National Science Foundation of China (11401461), Ministry of Science and Technology of China (2015DFA81780) and Fundamental Research Funds for the Central Universities (2015gjhz15). Shurong Zheng’s research was supported by The National Science Foundation of China (11522105 and 11690012). Dandan Jiang’s research was supported by The National Science Foundation of China (11471140). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.