TRACE: Relaying Structural State Beyond the Fixed Input Window for Non-stationary Time Series Forecasting

The reversible normalization family, from RevIN through SAN, FAN, and DDN, mitigates non-stationarity in real-world time series with progressively more precise restoration statistics, but each method estimates its correction quantities from the current input window alone. When the window is short, observation noise dominates the level and phase of the periodic components, and the forecast origin never uses observations before the window boundary. This work proposes TRACE, an adapter that carries the history preceding the window in a small structural state that is relayed from one forecast origin to the next. A fixed linear state-space filter with a per-channel level and $K$ harmonic components updates the state causally and has no learnable parameters; at forecast time the state is rolled out analytically and combined with the backbone forecast through a learned gate. Because the gate starts at zero, TRACE is initialized exactly at the backbone with window-statistic normalization and can learn to close the structural branch. The history reaches the state, but never the backbone, so this state continuity leaves the backbone's input length unchanged and is a design choice separate from window extension. Across four forecasting backbones, seven real-world benchmarks and three seeds, TRACE lowers the overall mean MSE by 10.66% against RevIN and by 6.10% against DDN, the strongest competing adapter, while using only 226-610 learnable parameters, 64-10,129 times fewer than SAN, FAN and DDN. Controlled experiments show that the gain depends on history the backbone never sees and that window-only forecasts combined in the same way do not reproduce it. The code is available at https://anonymous.4open.science/r/TRACE-8346.