Continuous-time attention improves long-term multivariate forecasting accuracy
CTIA-ODE: Continuous-Time Inter-Variable Attention for Long-Term Time Series Forecasting
Machine Learning
Summary
Forecasting multiple related measurements over time is useful but hard when outside factors change continuously. The authors present CTIA-ODE, a method that models how these factors evolve without forced time alignment, making predictions smoother and more accurate. They stabilize predictions by anchoring trends and reducing the impact of unusual extreme values. Tests on various real-world datasets show their method forecasts better and faster over long time spans than previous approaches.
What this means in practice
- •For financial analysts: Forecast complex financial indicators over long periods by capturing continuously evolving external economic factors more accurately.
- •For energy demand planners: Predict long-term energy usage with improved handling of varying external conditions like weather or policy changes without strict time alignment.
Authors
Chengyi Pan, Huangqimei Zheng, Hao Xue
Abstract
Although multivariate time series forecasting has broad application prospects, effectively incorporating exogenous variables remains challenging. Prevailing discrete-time architectures often impose rigid temporal alignment across heterogeneous variables, which may limit their ability to capture continuously evolving external effects. To address this limitation, we introduce CTIA-ODE, a continuous-time forecasting framework centered on Continuous-Time Inter-Variable Attention (CTIA). Specifically, CTIA is embedded within an ordinary differential equation (ODE) solver, enabling the continuously evolving endogenous trajectory to dynamically query a static exogenous context along the integration path without requiring explicit temporal alignment. To improve the stability of the continuous latent dynamics, we further introduce a dual-stabilization strategy: architecturally, a Linear Residual Augmentation (LRA) module provides a macroscopic trend anchor, while an Outlier-Robust Hybrid Loss (ORHL) mitigates the influence of heavy-tailed anomalies during optimization. Extensive experiments across eight real-world datasets demonstrate that CTIA-ODE achieves state-of-the-art forecasting performance across diverse datasets and prediction horizons, while maintaining a favorable accuracy-efficiency trade-off with a compact memory footprint and low inference latency, particularly under long-horizon forecasting settings. Anonymous code is available at https://anonymous.4open.science/r/CTIA-ODE-15A6/.