Trimmed Granger causality between two groups of time series

The identification of causal effects between two groups of time series has been an important topic in a wide range of applications such as economics, engineering, medicine, neuroscience, and biology. In this paper, a simplified causal relationship (called trimmed Granger causality) based on the context of Granger causality and vector autoregressive (VAR) model is introduced. The idea is to characterize a subset of “important variables” for both groups of time series so that the underlying causal structure can be presented based on minimum variable information. When the VAR model is specified, explicit solutions are provided for the identification of important variables. When the parameters of the VAR model are unknown, an efficient statistical hypothesis testing procedure is introduced to estimate the solution. An example representing the stock indices of different countries is used to illustrate the proposed methods. In addition, a simulation study shows that the proposed methods significantly outperform the Lasso-type methods in terms of the accuracy of characterizing the simplified causal relationship.