Time-varying Group Lasso Granger Causality Graph for High Dimensional Dynamic system

•To identify the structure change characteristics of causal relationships for time-varying networks, we propose dynamic network based on Granger causality for modeling the time-varying directed dependency structures.•For the structural learning problem of the proposed time-varying Granger causality graph, we introduce a kernel reweighted group lasso method. The method considers the group structure of the lagged variables and improves the accuracy and efficiency of the algorithm.•In addition, the time-varying Granger causality network is applied to financial field. The results show that networks based on Granger causality have rich indicators to characterize both the global evolution features of networks and the different functions of individual nodes in the graph. Feature selection is a crucial preprocessing step in data analysis and machine learning. Since causal relationships imply the underlying mechanism of a system, causality-based feature selection methods have gradually attracted great attentions. For a high dimensional system undergoing dynamic transformation, because of the non-stationarity and sample scarcity, modeling the causal structure among these features is difficult. In this paper, we propose a time-varying Granger causal networks to capture the causal relations underlying high dimensional time-varying vector autoregressive models with high order lagged dependence. A kernel reweighted group lasso method is proposed, which overcomes the limitations of sample scarcity and transforms the problem of Granger causal structural learning into a group variable selection problem. The asymptotic consistency of the proposed algorithm is proved. We apply the time-varying Granger causal networks to simulation experiments and real data in the financial market. The study demonstrates that the method provides an efficient tool to detect changes and analysis characters of causal dependency structure in network evolution.