Hierarchically Regularized Deep Forecasting
This addresses the problem of scalable and accurate hierarchical forecasting for multivariate time series applications, representing an incremental improvement over existing methods.
The paper tackles hierarchical forecasting of correlated time series by proposing a method that decomposes time series using a global basis set and models hierarchical constraints via coefficients, combined with a time-varying linear autoregressive model. It demonstrates significantly improved overall performance across hierarchy levels compared to state-of-the-art models on public datasets.
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.