This paper considers a class of structural equation models for times series data. The models allow nonlinear instantaneous effects and lagged effects. On the other hand, Granger-causality based methods do not allow instantaneous effects and a linear non-Gaussian method TS-LiNGAM (Hyvarinen et al., ICML2008, JMLR2010) assumes linear effects.
This paper introduces a model and procedure for learning instantaneous and lagged causal relationships among variables in a time series when each causal relationship is either identifiable in the sense of the additive noise model (Hoyer et al. 2009) or exhibits a time structure. The learning procedure finds a causal order by iteratively fitting VAR or GAM models where each variable is a function of all other variables and making the variable with the least dependence the lowest variable in the order. Excess parents are then pruned to produce the summary causal graph (where x->y indicates either an instantaneous or lagged cause up to the order of the VAR or GAM model that is fit). Experiments show that the method outperforms competing methods and returns no results in cases where the model can be identified (rather than wrong results).