A novel Granger causality method based on HSIC-Lasso for revealing nonlinear relationship between multivariate time series

The causality analysis is an important research topic in time series data mining. Granger causality analysis is a powerful method that determines cause and effect based on predictability. However, the traditional Granger causality is limited to analyzing linear causality between bivariate time series, because it is based on vector autoregressive models. In this paper, we propose a novel method, named Hilbert–Schmidt independence criterion Lasso Granger causality (HSIC-Lasso-GC), for revealing nonlinear causality between multivariate time series. Firstly, for each time series, we perform stationarity test and state space reconstruction to extract the historical information. Then, we build a HSIC-Lasso model of all input variables and output variable, where the optimal model is selected by generalized information criterion. Finally, according to the significance test, we get the causality analysis results from all input variables to output variable. In the simulations, we use two benchmark datasets and two actual datasets to test the effectiveness of the proposed method. The results show that the proposed method can effectively analyze nonlinear causality between multivariate time series.