  Hierarchical forecasting is a key problem in many practical multivariate
forecasting applications - the goal is to simultaneously predict a large number
of correlated time series that are arranged in a pre-specified aggregation
hierarchy. The main challenge is to exploit the hierarchical correlations to
simultaneously obtain good prediction accuracy for time series at different
levels of the hierarchy. In this paper, we propose a new approach for
hierarchical forecasting which consists of two components. First, decomposing
the time series along a global set of basis time series and modeling
hierarchical constraints using the coefficients of the basis decomposition. And
second, using a linear autoregressive model with coefficients that vary with
time. Unlike past methods, our approach is scalable (inference for a specific
time series only needs access to its own history) while also modeling the
hierarchical structure via (approximate) coherence constraints among the time
series forecasts. We experiment on several public datasets and demonstrate
significantly improved overall performance on forecasts at different levels of
the hierarchy, compared to existing state-of-the-art hierarchical models.
