We develop and evaluate an approach to causal modeling based on time series data, collectively referred to as "grouped graphical Granger modeling methods." Graphical Granger modeling uses graphical modeling techniques on time series data and invokes the notion of "Granger causality" to make assertions on causality among a potentially large number of time series variables through inference on time-lagged effects. The present paper proposes a novel enhancement to the graphical Granger methodology by developing and applying families of regression methods that are sensitive to group information among variables, to leverage the group structure present in the lagged temporal variables according to the time series they belong to. Additionally, we propose a new family of algorithms we call group boosting, as an improved component of grouped graphical Granger modeling over the existing regression methods with grouped variable selection in the literature (e.g group Lasso). The introduction of group boosting methods is primarily motivated by the need to deal with non-linearity in the data. We perform empirical evaluation to confirm the advantage of the grouped graphical Granger methods over the standard (non-grouped) methods, as well as that specific to the methods based on group boosting. This advantage is also demonstrated for the real world application of gene regulatory network discovery from time-course microarray data.