Forecasting time series with constraints
This work addresses the problem of improving forecast accuracy with constraints for applications such as energy and tourism, representing an incremental advancement over existing constraint-based methods.
The paper tackles the challenge of integrating linear constraints into time series forecasting by proposing a unified framework that efficiently computes the exact minimizer of constrained empirical risk using linear algebra, achieving state-of-the-art performance in tasks like electricity demand and tourism forecasting.
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.