{"ID":6626554,"CreatedAt":"2026-07-15T02:56:36.47817413Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.13006","arxiv_id":"2607.13006","title":"The Spectrum Is Not Enough: When Context Helps Time-Series Forecasting","abstract":"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 $+33\\%\\!\\to\\!-35\\%$, $p{\u003c}10^{-40}$) 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://anonymous.4open.science/r/SINE.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2607.13006","url_pdf":"https://arxiv.org/pdf/2607.13006v1","authors":"[\"Mert Onur Cakiroglu\",\"Mehmet Dalkilic\",\"Hasan Kurban\"]","published":"2026-07-14T17:50:28Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","project_urls":"[\"https://anonymous.4open.science/r/SINE\"]","has_code":false}