Hierarchically Regularized Deep Forecasting

TL;DR

This paper introduces a scalable hierarchical forecasting method that decomposes time series into basis components and models their coefficients with time-varying autoregressive models, improving accuracy across hierarchy levels.

Contribution

It proposes a novel, scalable approach combining basis decomposition and time-varying autoregressive models to enhance hierarchical forecasting accuracy.

Findings

Significantly improved forecast accuracy across hierarchy levels.

Scalable inference requiring only individual time series history.

Effective modeling of hierarchical constraints via basis coefficients.

Abstract

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.