Multivariate Causality Tests with Simulation and Application

The traditional linear Granger causality test has been widely used to examine the linear causality among several time series in bivariate settings as well as multivariate settings. Hiemstra and Jones (1994) develop a nonlinear Granger causality test in a bivariate setting to investigate the nonlinear causality between stock prices and trading volume. In this paper, we first discuss linear causality tests in multivariate settings and thereafter develop a nonlinear causality test in multivariate settings. A Monte Carlo simulation is conducted to demonstrate the superiority of our proposed multivariate test over its bivariate counterpart. In addition, we illustrate the applicability of our proposed test to analyze the relationships among different Chinese stock market indices