We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the graph structure is learned recursively without the need for cross-validation or parameter tuning by building upon a hyperparameter-free framework. Our approach does not require the graph to be undirected and also accommodates varying noise levels across different nodes.Experiments using real-world datasets show that the proposed method offers significant performance gains in prediction, in comparison with the graphs frequently associated with these datasets.