HypLTSF shows improved long-term time series forecasting with geometric hierarchy
HypLTSF: A Hyperbolic Geometric View of Multi-Scale Hierarchies for Long-Term Time Series Forecasting
Machine Learning
Summary
Forecasting long-term trends in time series data is hard because patterns happen at many different time scales that form hierarchies. The authors created HypLTSF, a method that represents these different scales as points in a special curved space called a Poincaré ball, which naturally fits hierarchical data better than flat spaces. They add rules so that points closer to the center represent more abstract, broader patterns, while points further out capture finer details. Their experiments show this helps predict future data more accurately over long periods.
What this means in practice
- •For energy grid planners: Improve accuracy in forecasting electricity demand over months by representing consumption patterns at multiple timescales with a hierarchical geometric model.
- •For financial analysts: Enhance long-range asset price predictions by explicitly modeling hierarchical temporal structures in market data using hyperbolic embeddings.
Authors
Namwoo Kim, Hyungryul Baik, Yoonjin Yoon
Abstract
Multi-scale modeling has become an effective approach for long-term time series forecasting, capturing temporal patterns that range from fine-grained local dynamics to coarse global trends. Representations across these temporal scales are inherently hierarchical, with coarser scales abstracting and aggregating information from finer ones. While existing approaches readily exchange information across these scales, the hierarchy itself is typically left as an emergent byproduct of such interactions rather than captured as a geometric structure in its own right. In this paper, we introduce HypLTSF, a framework that endows the multi-scale hierarchy with a concrete geometric form by embedding scale-wise representations into the Poincaré ball, whose exponentially expanding volume naturally accommodates hierarchical structures. To align this geometry with the temporal hierarchy, HypLTSF imposes two constraints: (1) a radial constraint that orders embeddings by their level of abstraction, and (2) an angular constraint that groups fine-scale patterns sharing a common coarser-scale ancestor. Extensive experiments on long-term time series forecasting benchmarks show that HypLTSF achieves state-of-the-art performance, suggesting that explicitly modeling the multi-scale hierarchy as a geometric structure is effective for forecasting.