Identification of nonlinear VAR models using general conditional independence graphs

The general conditional independence graphs are proposed for identifying nonlinear vector autoregressive model, which extend the graphical modeling approach for linear structure VAR. The conditional independence relations between time series variables and their lags can be tested efficiently and consistently using conditional mutual information statistics and a permutation procedure. Furthermore, a statistic resulted from the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity of the dependence. A bootstrap method based on surrogate data is used to determine the significance of the nonlinear test statistic. The finite sample behavior of the procedure through simulation time series with different linear and nonlinear dependence relations is investigated.