SAWS: Forecasting Inaccurate Time Series with Sharpness-Aware Weak Supervision

Inaccurate observations degrade time-series forecasting twice: inaccurate historical observations obscure the dynamics to predict, and inaccurate future observations used as labels degrade supervision. While applying means of observation accuracy improvement can recover useful information, treating resulting improved observations as ground-truth observations can amplify any errors that may have been introduced. We introduce SAWS, a forecasting framework that combines vector-quantized historical retrieval with sharpness-aware weak supervision. A past-only codebook compresses similar historical contexts and their observed dynamics into coordinate-supported prototypes. Retrieved prototypes correct inputs and supply weak targets without accessing the current forecast horizon. A detached, sample-level sharpness score measures the sensitivity of an exponential-moving-average forecaster on observed targets; together with prototype support and dispersion, it controls the influence of weak supervision. Multiscale temporal features preserve the distinction between short-term dynamics and longer-term context without requiring dense attribute-graph propagation. We characterize the bias–variance tradeoff of prototype completion and establish when sharpness weighting reduces weak-label error, explicitly contending with selection bias and confidence miscalibration. A leakage-controlled experimental evaluation offers evidence that SAWS is able to offer better accuracy and reliability on inaccurate data than are state-of-the-art baselines.