# The Spectrum Is Not Enough: When Context Helps Time-Series Forecasting

arXiv: https://arxiv.org/abs/2607.13006 · HTML: https://mlsanity.com/paper/2607.13006/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 37 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [Retrieval Augmented Time Series Forecasting](https://mlsanity.com/paper/2411.08249/) (2024)
- [Retrieval-Augmented Diffusion Models for Time Series Forecasting](https://mlsanity.com/paper/2410.18712/) (2024)
- [Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning](https://mlsanity.com/paper/2505.11349/) (2025)
- [Attractor Memory for Long-Term Time Series Forecasting: A Chaos Perspective](https://mlsanity.com/paper/2402.11463/) (2024)
- [Channel Dependence, Limited Lookback Windows, and the Simplicity of Datasets: How Biased is Time Series Forecasting?](https://mlsanity.com/paper/2502.09683/) (2025)
- [There are no Champions in Supervised Long-Term Time Series Forecasting](https://mlsanity.com/paper/2502.14045/) (2025)
- [LETS Forecast: Learning Embedology for Time Series Forecasting](https://mlsanity.com/paper/2506.06454/) (2025)
- [Exploring Accuracy Law for Deep Time Series Forecasters: An Empirical Study](https://mlsanity.com/paper/2510.02729/) (2025)
- [Frequency Matters: When Time Series Foundation Models Fail Under Spectral Shift](https://mlsanity.com/paper/2511.05619/) (2025)
- [Spectral Predictability as a Fast Reliability Indicator for Time Series Forecasting Model Selection](https://mlsanity.com/paper/2511.08884/) (2025)
- [Channel-wise Retrieval for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2604.05543/) (2026)
- [Why Do Time Series Models Need Long Context Windows?](https://mlsanity.com/paper/2606.01999/) (2026)
- [Multivariate de Bruijn Graphs: A Symbolic Graph Framework for Time Series Forecasting](https://mlsanity.com/paper/2505.22768/) (2025)
- [Retrieval Mechanisms Surpass Long-Context Scaling in Time Series Forecasting](https://mlsanity.com/paper/2605.08217/) (2026)
- [On Identifying Why and When Foundation Models Perform Well on Time-Series Forecasting Using Automated Explanations and Rating](https://mlsanity.com/paper/2508.20437/) (2025)
- [Beyond Model Ranking: Predictability-Aligned Evaluation for Time Series Forecasting](https://mlsanity.com/paper/2509.23074/) (2025)
- [Forecastability as an Information-Theoretic Limit on Prediction](https://mlsanity.com/paper/2603.27074/) (2026)

## 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