A new test of multivariate nonlinear causality

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.

Linear and nonlinear growth determinants: The case of Mongolia and its connection to China

“…Given the above VECM model, we examine the causalities from GDP t C , Coal t , and ∆Y t = ∆GDP t M , were the symbol ∆ denotes the first-order difference of a time series. We next adopt the following VECM model ( ) = 0( 02 ∶ ( ) = 0) and 03 : = 0( 04 ∶ = 0) to identify a Granger causality by applying a likelihood ratio LR-test (see Bai et al, 2010Bai et al, , 2011Bai et al, , 2018 . Under the assumption that the time series vector variables X t = (X 1,t , … , X 7,t )′ and Y t are strictly stationary, weakly dependent, and satisfy the mixing conditions stated in Denker and Keller (1983), we can test the null hypothesis that Y t does not strictly Granger cause X t = (X 1,t , … , X 7,t ) ′ .…”

“…Readers may refer to Bai et al (2010Bai et al ( , 2011Bai et al ( , 2018 for more details regarding the test statistic (4.5) and the definitions of C 1 , C 2 , C 3 , and C 4 .…”

Do Both Demand-Following and Supply-Leading Theories Hold True in Developing Countries?

“…Thereafter, one could test the null hypothesis 0 : ( ) = 0( 0 ∶ ( ) = 0) and/or 0 : = 0( 0 ∶ = 0) to identify Granger causality relation using the LR test. Bai, et al (2010Bai, et al ( , 2011Bai, et al ( , 2018 and extend the nonlinear causality test developed by Hiemstra and Jones (1994) and others to the multivariate setting. To identify any nonlinear Granger causality relationship from any two series, say { } and { } in the bivariate setting, one has to first apply the linear model to { } and { } to identify their linear causal relationships and obtain the corresponding residuals, {̂1 } and {̂2 }.…”

“…Granger causality test (Bai, et al, 2010(Bai, et al, , 2011(Bai, et al, , 2018 to investigate the presence of nonlinear causal relations between financial development and economic growth. To test whether both demand-following supply-leading theories hold true, in this paper we also suggest the use of a cointegration technique and examine whether there is any cointegration between financial development and economic growth.…”

Moment Generating Function, Expectation and Variance of Ubiquitous Distributions with Applications in Decision Sciences: A Review

“…Wong, and Zhang (2011) first discuss linear causality tests in multivariate settings and thereafter develop a nonlinear causality test in multivariate settings Bai, Hui, Jiang, Lv, Wong, Zheng (2018). revisit the issue by estimating the probabilities and reestablish the CLT of the new test statistic Hui, Wong, Bai, and Zhu (2017).…”