aiqbench analysis
TimeES introduces a novel framework leveraging evolutionary spectra theory to address the non-stationarity and uncertainty inherent in real-world time series forecasting. By explicitly modeling frequency evolution and exploiting spectral sparsity, this approach improves both deterministic trajectory prediction and probabilistic uncertainty quantification while maintaining computational efficiency. The method demonstrates state-of-the-art performance across diverse tasks, offering a significant advancement for deep learning models that require explicit handling of temporal dynamics.
TimeES: Probabilistic and Deterministic Time Series Forecasting via Evolutionary Spectra
arXiv:2609.32384v1 Announce Type: new 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.
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: this https URL.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2609.32384 [cs.LG]
(or arXiv:2609.32384v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.32384 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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