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

Abstract

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.