Forecasting time series with constraints

TL;DR

This paper introduces a unified, scalable framework for incorporating linear constraints into time series forecasting models, enabling efficient computation and achieving state-of-the-art results on real-world datasets.

Contribution

It presents a novel, unified approach for integrating linear constraints into time series forecasting, with efficient algorithms and GPU optimization.

Findings

Achieves state-of-the-art performance on electricity demand forecasting.

Provides an efficient method for computing constrained empirical risk minimizers.

Demonstrates scalability and effectiveness on real-world datasets.

Abstract

Time series forecasting presents unique challenges that limit the effectiveness of traditional machine learning algorithms. To address these limitations, various approaches have incorporated linear constraints into learning algorithms, such as generalized additive models and hierarchical forecasting. In this paper, we propose a unified framework for integrating and combining linear constraints in time series forecasting. Within this framework, we show that the exact minimizer of the constrained empirical risk can be computed efficiently using linear algebra alone. This approach allows for highly scalable implementations optimized for GPUs. We validate the proposed methodology through extensive benchmarking on real-world tasks, including electricity demand forecasting and tourism forecasting, achieving state-of-the-art performance.