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TimeES: Probabilistic and Deterministic Time Series Forecasting via Evolutionary Spectra

NeurIPS 2026 · Time series › Causal and generative time series · approach: Probabilistic and conformal forecasting · 0 citations (OpenAlex)

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Proposes TimeES, a linear-backbone forecaster built on a discrete evolutionary spectra (DES) generative model with Hermitian-symmetry and energy-based frequency selection, supporting both probabilistic and deterministic time series forecasting.

Problem

Deep forecasters ignore the evolution and randomness of Fourier spectra in non-stationary time series, limiting both point forecast accuracy and calibrated uncertainty estimation.

Approach

Recasts evolutionary spectra theory as a parameterized discrete generative model where a network estimates a time-varying amplitude matrix over a reduced set of energy-selected frequencies (Hermitian symmetry), and random complex Gaussian weights yield probabilistic samples while fixing them yields deterministic decomposition.

Key results

• On probabilistic forecasting across nine datasets, TimeES reports a 17.23% average CRPS reduction and 18.66% MSE reduction versus baselines, with best CRPS on 8 of 9 datasets.
• On single-variate long-term forecasting, TimeES achieves state-of-the-art MSE on 8 of 9 datasets, improving on FreTS by 19.38% on average.
• Plugging TimeES into iTransformer on ETTh1 reduces average MSE by 2.84% (0.454 to 0.441).

Surprising findings

• The ILI dataset shows only marginal gains, which the authors attribute to limited sample size hindering reliable evolutionary spectra estimation.

Limitations

• Frequency selection may be ineffective under high-noise conditions where energy does not concentrate in few frequencies.
• Learning evolutionary spectra requires sufficient data; performance is limited on small datasets such as ILI.
• Uses a standard simple linear architecture without specialized design for evolutionary spectra dynamics.

Experimental setup

Datasets: ETTm1 ETTm2 ETTh1 ETTh2 ECL EXG Traffic Weather Solar ILI UEA

Benchmarks: ETTm1 ETTm2 ETTh1 ETTh2 ECL EXG ILI Solar Traffic Weather

Metrics: CRPS MSE MAE QICE

Baselines: TimeGrad CSDI TimeDiff DiffusionTS TMDM NsDiff Autoformer FEDformer TimesNet FITS FreTS PatchTST

Builds on: evolutionary spectra theory short-time Fourier transform discrete Fourier transform FreTS NsDiff

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