TimeES: Probabilistic and Deterministic Time Series Forecasting via Evolutionary Spectra
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Abstract (arXiv)
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.
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References · 48
- 2020Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecastingcited by 2,169
- 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 2,039
- 2021Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecastingcited by 1,676
- 2022FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecastingcited by 1,210
- 2022TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysiscited by 1,058
- 2023iTransformer: Inverted Transformers Are Effective for Time Series Forecastingcited by 931
- 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
- 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 494
- 2022Non-stationary Transformers: Exploring the Stationarity in Time Series Forecastingcited by 391
- 2024TimeMixer: Decomposable Multiscale Mixing for Time Series Forecastingcited by 346
- 2018The UEA multivariate time series classification archive, 2018cited by 338
- 2021SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interactioncited by 338
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- 2021Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecastingcited by 337
- 2024TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variablescited by 248
- 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 198
- 2023FITS: Modeling Time Series with 10k Parameterscited by 195
- 2024Diffusion-TS: Interpretable Diffusion for General Time Series Generationcited by 184
- 2023Frequency-domain MLPs are More Effective Learners in Time Series Forecastingcited by 172
- 2023Diffusion Schr"odinger Bridge Matchingcited by 153
- 2021TimeVAE: A Variational Auto-Encoder for Multivariate Time Series Generationcited by 142
- 2023Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Surveycited by 140
- 2016C-RNN-GAN: Continuous recurrent neural networks with adversarial trainingcited by 132
- 2021AdaRNN: Adaptive Learning and Forecasting of Time Seriescited by 121
- 2023Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictorscited by 113
- 2024DUET: Dual Clustering Enhanced Multivariate Time Series Forecastingcited by 107
- 2022CARD: Classification and Regression Diffusion Modelscited by 103
- 2023Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecastingcited by 93
- 2022Spatio-Temporal Meta-Graph Learning for Traffic Forecastingcited by 88
- 2023Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecastingcited by 88
- 2023Non-autoregressive Conditional Diffusion Models for Time Series Predictioncited by 78
- 2022Multivariate Time Series Forecasting with Dynamic Graph Neural ODEscited by 72
- 2024A Survey on Diffusion Models for Time Series and Spatio-Temporal Datacited by 67
- 2024Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processescited by 66
- 2023SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecastingcited by 55
- 2023Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEscited by 49
- 2024Frequency Adaptive Normalization For Non-stationary Time Series Forecastingcited by 47
- 2024FilterNet: Harnessing Frequency Filters for Time Series Forecastingcited by 47
- 2023A Survey on Deep Learning based Time Series Analysis with Frequency Transformationcited by 40
- 2022Koopman Neural Forecaster for Time Series with Temporal Distribution Shiftscited by 37
- 2022A review of predictive uncertainty estimation with machine learningcited by 29
- 2023Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputationcited by 27
- 2023Spatial-Temporal-Decoupled Masked Pre-training for Spatiotemporal Forecastingcited by 27
- 2025Non-stationary Diffusion For Probabilistic Time Series Forecastingcited by 27
- 2024Heterogeneity-Informed Meta-Parameter Learning for Spatiotemporal Time Series Forecastingcited by 18
- 2024Deep Frequency Derivative Learning for Non-stationary Time Series Forecastingcited by 13
- 2025Diffusion Models for Time Series Forecasting: A Surveycited by 11
- 2021Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertaintiescited by 4
- 2025SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecastingcited by 2
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