The need for mining causality, beyond mere statistical correlations, for real world problems has been recognized widely. Many of these applications naturally involve temporal data, which raises the challenge of how best to leverage the temporal information for causal modeling. Recently graphical modeling with the concept of “Granger causality”, based on the intuition that a cause helps predict its effects in the future, has gained attention in many domains involving time series data analysis. With the surge of interest in model selection methodologies for regression, such as the Lasso, as practical alternatives to solving structural learning of graphical models, the question arises whether and how to combine these two notions into a practically viable approach for temporal causal modeling. In this paper, we examine a host of related algorithms that, loosely speaking, fall under the category of graphical Granger methods, and characterize their relative performance from multiple viewpoints. Our experiments show, for instance, that the Lasso algorithm exhibits consistent gain over the canonical pairwise graphical Granger method. We also characterize conditions under which these variants of graphical Granger methods perform well in comparison to other benchmark methods. Finally, we apply these methods to a real world data set involving key performance indicators of corporations, and present some concrete results.