ECL

Impossibility result: spectral predictability indices cannot predict when context, retrieval, or foundation models help in time-series forecasting

A new arXiv preprint proves an impossibility result showing that power-spectrum-based predictability indices cannot determine whether adding context (longer lookback, retrieval, or pretrained models) will improve time-series forecasting, because such indices are invariant under phase randomization while the value of retrieval and foundation models is not. The authors introduce a label-free diagnostic called the 'coverage deficit' that measures beyond-spectrum structure as the gain of analog over linear prediction. Experiments across seven benchmarks validate the distinction: retrieval value collapses under spectrum-preserving surrogates while spectral indices remain frozen, and the new diagnostic predicts the sign of beyond-spectrum value where spectral indices fail. No new forecaster is introduced; the contribution is the theoretical distinction, controlled comparisons, and a deployment diagnostic.