The Spectrum Is Not Enough: When Context Helps Time-Series Forecasting
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Abstract (arXiv)
A growing family of indices scores how predictable a series is from its spectrum. Practitioners increasingly read these scores as answering a different question: whether adding context, a longer lookback, a retrieval plug-in, or a pretrained model, will help. These are not the same question. The value of context is a property of the operating point, not of the series. Any index built from the power spectrum is invariant under phase randomization, whereas the beyond-second-order value that retrieval and foundation models supply is not, because a phase-randomized series is asymptotically Gaussian. We state this as an impossibility result and isolate it with surrogate pairs that fix the spectrum and the marginal by construction. We then give a label-free, configuration-level diagnostic, the coverage deficit, whose principal term measures beyond-spectrum structure as the gain of analog over linear prediction. On seven benchmarks the prediction holds: window-keyed retrieval's value collapses across surrogate pairs (ECL median +33%!→!-35%, p<10-40) while every spectral index stays frozen; a foundation model's value splits into a surviving second-order part and a small beyond-linear margin that collapses; a longer linear window's value survives. Leave-one-dataset-out, the structure term predicts the sign of beyond-spectrum value where the spectral indices trail it, and the reverse holds for the second-order mechanism. We introduce no new forecaster; the contribution is the distinction, a controlled comparison, and a diagnostic for the deployment decision. Code: https://github.com/KurbanIntelligenceLab/SINE
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 22 of its 37 references that are in the map. First posted on arXiv 14 Jul 2026.
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22 of 37 references.
References · 22
- 2022A Time Series is Worth 64 Words: Long-term Forecasting with Transformerscited by 1,981
- 2022Are Transformers Effective for Time Series Forecasting?cited by 1,400
- 2024Unified Training of Universal Time Series Forecasting Transformerscited by 588
- 2024CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patternscited by 102
- 2024Frequency Adaptive Normalization For Non-stationary Time Series Forecastingcited by 45
- 2024Retrieval Augmented Time Series Forecastingcited by 40
- 2024Retrieval-Augmented Diffusion Models for Time Series Forecastingcited by 35
- 2024Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspectivecited by 17
- 2025Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learningcited by 14
- 2025There are no Champions in Supervised Long-Term Time Series Forecastingcited by 8
- 2025Channel Dependence, Limited Lookback Windows, and the Simplicity of Datasets: How Biased is Time Series Forecasting?cited by 6
- 2025LETS Forecast: Learning Embedology for Time Series Forecastingcited by 5
10 more
- 2025Exploring Accuracy Law for Deep Time Series Forecasters: An Empirical Studycited by 4
- 2025Frequency Matters: When Time Series Foundation Models Fail Under Spectral Shiftcited by 3
- 2025Spectral Predictability as a Fast Reliability Indicator for Time Series Forecasting Model Selectioncited by 3
- 2026Channel-wise Retrieval for Multivariate Time Series Forecastingcited by 3
- 2025Multivariate de Bruijn Graphs: A Symbolic Graph Framework for Time Series Forecastingcited by 2
- 2026Retrieval Mechanisms Surpass Long-Context Scaling in Time Series Forecastingcited by 2
- 2026Why Do Time Series Models Need Long Context Windows?cited by 2
- 2025On Identifying Why and When Foundation Models Perform Well on Time-Series Forecasting Using Automated Explanations and Ratingcited by 1
- 2025Beyond Model Ranking: Predictability-Aligned Evaluation for Time Series Forecastingcited by 1
- 2026Forecastability as an Information-Theoretic Limit on Predictioncited by 1
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