To exhibit the leading/lagging relationship among groups in a VAR process, we construct a three-group causal path (an extended Granger causality) as well as an identi cation procedure for the pathway which includes the independent, the intermediate and the dependent groups. In addition, we impose the unidirectional restriction on the pathway. Consequently, our method can organize more detailed and practical causal structure in a dynamic system than the conventional methods. The property concerning the impulse response function is derived when the three-group causality occurs in the VAR model. Finally, we show that these techniques can be easily implemented in the U.S. economic model consisting of the stock return, the inflation rate and the industrial production growth rate.
International Journal of Innovative Computing, Information and Control, 7(5) , 2563-2577