SPImpute: Structure-Preserving History Imputation for Frozen Time Series Forecasting

Time series foundation models forecast from history, but missing intervals can change their predictions. Existing imputers often focus on reconstruction error without considering how well downstream models can use the data. We propose SPImpute to fill missing values from observed history and a given period. Its sparse quadratic reconstruction combines local differences with reference increments across periods. Decomposing the correction penalty identifies when missing intervals interact and when the penalty reduces to degree-weighted reference-value fidelity. For eligible long gaps, a same-phase candidate corrects donor levels when all available donors lie on one side of the missing position. Masked validation tasks re-estimate drift. If correction leaves the actual candidate unchanged, SPImpute retains the original procedure. Extensive experiments show its effectiveness. On nineteen series at five missing rates, SPImpute ranks first among 21 imputers under two foundation models, with mean MSE ranks of 5.39 and 6.38. MSE reductions relative to Linear, averaged equally across data sources, are 10.81%, 10.11%, and 2.69% under Sundial, TimesFM-2.5, and Chronos-2, respectively. Independent experiments confirm conditional coupling gains for repeated pulse gaps. We compare same-phase correction with the uncorrected procedure using 1,152 synthetic histories. Across 24 drift settings near the forecast origin, mean relative MSE reductions are 92.9% and 94.9% under TimesFM-2.5 and Chronos-2, respectively; all 576 interior-gap inputs remain unchanged. Median CPU imputation time is 78.66 ms.