  Graph-based deep learning methods have become popular tools to process
collections of correlated time series. Differently from traditional
multivariate forecasting methods, neural graph-based predictors take advantage
of pairwise relationships by conditioning forecasts on a (possibly dynamic)
graph spanning the time series collection. The conditioning can take the form
of an architectural inductive bias on the neural forecasting architecture,
resulting in a family of deep learning models called spatiotemporal graph
neural networks. Such relational inductive biases enable the training of global
forecasting models on large time-series collections, while at the same time
localizing predictions w.r.t. each element in the set (i.e., graph nodes) by
accounting for local correlations among them (i.e., graph edges). Indeed,
recent theoretical and practical advances in graph neural networks and deep
learning for time series forecasting make the adoption of such processing
frameworks appealing and timely. However, most of the studies in the literature
focus on proposing variations of existing neural architectures by taking
advantage of modern deep learning practices, while foundational and
methodological aspects have not been subject to systematic investigation. To
fill the gap, this paper aims to introduce a comprehensive methodological
framework that formalizes the forecasting problem and provides design
principles for graph-based predictive models and methods to assess their
performance. At the same time, together with an overview of the field, we
provide design guidelines, recommendations, and best practices, as well as an
in-depth discussion of open challenges and future research directions.
