Timees improves forecasting accuracy and uncertainty modeling for changing time series
TimeES: Probabilistic and Deterministic Time Series Forecasting via Evolutionary Spectra
Machine LearningArtificial Intelligence
Summary
Time series data, like weather or stock prices, often change their patterns over time and have uncertainty that evolves. The authors designed TimeES, a new method that looks at these changes using a special Fourier-based approach called evolutionary spectra. This allows TimeES to predict what might happen next and also give a better estimate of how uncertain those predictions are. Their approach is faster, easier to understand, and works well on different forecasting tasks.
What this means in practice
- •For financial data analysts: Forecast stock or economic indicators with better uncertainty estimation in non-stationary market conditions.
- •For energy demand planners: Improve predictions of fluctuating energy consumption by capturing evolving patterns in usage data.
Authors
Weiwei Ye, Renhe Jiang, Hangchen Liu, Dongyuan Li, Yoshihide Sekimoto
Abstract
Real-world time series are inherently non-stationary, with trends, periodic patterns, and uncertainty evolving over time. While the Fourier domain offers a natural lens to model time series, current deep learning approaches do not explicitly model evolution and randomness in the Fourier spectra, which limits their ability to accurately predict both the expected trajectory and its uncertainty in non-stationary time series. Motivated by Evolutionary Spectra (ES) theory, we propose TimeES, a general framework that enables probabilistic and deterministic forecasting via the evolutionary spectra theory. Specifically, we derive a parameterizable evolutionary spectra formulation, recasting non-stationary random process modeling as learning an evolving representation modulated by random variables. Furthermore, we reduce the complexity of the estimated spectra from O(NM) to O(NK), where K << M/2, by exploiting Hermitian symmetry and spectral energy sparsity for frequency selection. Based on a simple linear backbone, our proposed TimeES achieves consistent state-of-the-art performance across both deterministic and probabilistic forecasting tasks, with high efficiency and interpretability. Code is available at: https://github.com/wwy155/TimeES.