Learning causal graphs of nonlinear structural vector autoregressive model using information theory criteria

Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis. Traditional causality inference methods have a salient limitation that the model must be linear and with Gaussian noise. Although additive model regression can effectively infer the nonlinear causal relationships of additive nonlinear time series, it suffers from the limitation that contemporaneous causal relationships of variables must be linear and not always valid to test conditional independence relations. This paper provides a nonparametric method that employs both mutual information and conditional mutual information to identify causal structure of a class of nonlinear time series models, which extends the additive nonlinear times series to nonlinear structural vector autoregressive models. An algorithm is developed to learn the contemporaneous and the lagged causal relationships of variables. Simulations demonstrate the effectiveness of the proposed method.