  Existing relationships among time series can be exploited as inductive biases
in learning effective forecasting models. In hierarchical time series,
relationships among subsets of sequences induce hard constraints (hierarchical
inductive biases) on the predicted values. In this paper, we propose a
graph-based methodology to unify relational and hierarchical inductive biases
in the context of deep learning for time series forecasting. In particular, we
model both types of relationships as dependencies in a pyramidal graph
structure, with each pyramidal layer corresponding to a level of the hierarchy.
By exploiting modern - trainable - graph pooling operators we show that the
hierarchical structure, if not available as a prior, can be learned directly
from data, thus obtaining cluster assignments aligned with the forecasting
objective. A differentiable reconciliation stage is incorporated into the
processing architecture, allowing hierarchical constraints to act both as an
architectural bias as well as a regularization element for predictions.
Simulation results on representative datasets show that the proposed method
compares favorably against the state of the art.
