The Spectrum Is Not Enough: When Context Helps Time-Series Forecasting
2026-07-14 • Machine Learning
Machine Learning
AI summaryⓘ
The authors explain that existing measures which use a series' spectrum to judge predictability don't tell us whether adding extra context or advanced models will improve predictions. They show that such spectral measures can't detect improvements from beyond-second-order structures because these become hidden when the data's phase is randomized. To address this, they propose a new diagnostic called the coverage deficit that better identifies when extra context or complex models can help. Their experiments confirm this distinction, helping guide when to use more advanced forecasting methods.
power spectrumphase randomizationsecond-order statisticsforecastinglinear predictionretrieval modelsfoundation modelssurrogate pairscoverage deficittime series predictability
Authors
Mert Onur Cakiroglu, Mehmet Dalkilic, Hasan Kurban
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 $+33\%\!\to\!-35\%$, $p{<}10^{-40}$) 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.