AI 中文总结
研究时间序列预测中上下文的作用，指出频谱指标与添加上下文等因素回答的问题不同，通过替代对等给出覆盖不足诊断，在七个基准测试中验证，表明窗口键控检索等情况，为部署决策提供区分、比较及诊断。
AI 中文摘要
越来越多的指标用于衡量一个序列从其频谱的可预测性。从业者越来越将这些分数解读为另一个不同的问题：即添加上下文、更长的回溯、检索插件或预训练模型是否会有帮助。但这并非同一个问题。上下文的价值是操作点的属性，而非序列的属性。任何基于功率谱构建的指标在相位随机化下都是不变的，而检索和基础模型提供的二阶以上的值并非如此，因为相位随机化序列渐近高斯。我们将此表述为一个不可能结果，并用构造固定频谱和边缘的替代对将其分离。然后我们给出了一个无标签、配置级别的诊断——覆盖不足，其主要项将超出频谱的结构衡量为类比线性预测的增益。在七个基准测试中预测成立：窗口键控检索的值在替代对之间崩溃（ECL中位数从+33%变为 -35%，p < 10^-40），而每个频谱指标保持不变；基础模型的值分为一个留存的二阶部分和一个崩溃的小的超线性边缘；更长的线性窗口的值留存。留一数据集法中，结构项预测超出频谱值的符号，频谱指标则落后，二阶机制则相反。我们没有引入新预测器；贡献在于区分、受控比较以及用于部署决策的诊断。代码：此https网址。
英文摘要
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
