  We present Bayesian Spillover Graphs (BSG), a novel method for learning
temporal relationships, identifying critical nodes, and quantifying uncertainty
for multi-horizon spillover effects in a dynamic system. BSG leverages both an
interpretable framework via forecast error variance decompositions (FEVD) and
comprehensive uncertainty quantification via Bayesian time series models to
contextualize temporal relationships in terms of systemic risk and prediction
variability. Forecast horizon hyperparameter $h$ allows for learning both
short-term and equilibrium state network behaviors. Experiments for identifying
source and sink nodes under various graph and error specifications show
significant performance gains against state-of-the-art Bayesian Networks and
deep-learning baselines. Applications to real-world systems also showcase BSG
as an exploratory analysis tool for uncovering indirect spillovers and
quantifying systemic risk.
