判断时间序列预测能否靠上下文提升，不能只看频谱，要看超越频谱的结构信息。
The Spectrum Is Not Enough: When Context Helps Time-Series Forecasting
- 用频谱不变的替代对，隔离出超出二阶统计量的结构信息
- 提出覆盖缺陷诊断指标，可量化上下文带来的非线性增益
- 实验证明检索和大模型的价值主要来自非频谱结构，适合部署决策参考
越来越多的指标基于频谱评估序列可预测性。从业者常将这些指标误用于判断添加上下文（如更长历史、检索模块或预训练模型）是否有效，但二者本质不同。任何仅依赖功率谱的指标在相位随机化下保持不变，而检索与基础模型提供的超越二阶统计量的信息则不具此性质，因相位随机化后序列渐近于高斯分布。本文提出不可能性结果，并构造频谱与边缘分布固定的替代对以分离该效应。进一步提出无需标签的配置级诊断——覆盖缺陷，其主项衡量模拟预测相对于线性预测的增益，即超越频谱的结构。在七个基准上验证：窗口键检索价值在替代对间崩溃（ECL中位数从+33%降至-35%，p<10⁻⁴⁰），而所有谱指数保持不变；基础模型价值分解为残留的二阶部分与微小的非线性余量，后者也崩溃；更长线性窗口的价值仍存在。留一数据集外分析表明，结构项能预测超越频谱价值的正负，而谱指数无法做到，反之亦然。本文不引入新预测器，贡献在于厘清区别、实现受控对比及提供部署诊断工具。代码：https://github.com/KurbanIntelligenceLab/SINE
原文摘要 · Abstract (English)
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 \emph{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 $+33\%\!\to\!-35\%$, $p{<}10^{-40}$) 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
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