Long-term time series forecasting improves with hierarchical geometry approach
HypLTSF: A Hyperbolic Geometric View of Multi-Scale Hierarchies for Long-Term Time Series Forecasting
Machine Learning
Summary
Predicting events far into the future from time-based data is tricky because patterns happen at different levels, like small daily changes and big long-term trends. The authors found that organizing these patterns into a clear hierarchy using a special curved space called the Poincaré ball helps keep this structure clear. They developed a method, HypLTSF, that arranges information so that detailed patterns stay near the edges and broader trends stay toward the center. This geometric approach made their predictions more accurate compared to previous methods.
time series forecastingmulti-scale modelinghierarchical structurePoincaré ballhyperbolic geometryradial constraintangular constraintlong-term predictiontemporal patterns
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.