Bayes Averaging or Over-Smoothing? Excessive Contraction in Time Series Forecasting

Time series forecasting models often produce predictions that vary much less than observed futures, a behavior commonly interpreted as over-smoothing. Yet under squared loss, even the Bayes-optimal predictor averages over plausible futures, reducing variation under target uncertainty. Reduced variation alone therefore does not establish a modeling deficiency. We develop a Bayes-referenced framework for variation *across* predictions for similar inputs and *within* individual forecast trajectories. For both perspectives, we derive an observable criterion that relates predictive amplitude to target alignment and identifies excessive contraction along the model's current prediction direction, without directly estimating the Bayes-optimal predictor. Using the proposed contraction measures, we examine eight forecasting models across six benchmark datasets and confirm that predictive contraction is widespread and that stronger contraction is consistently associated with larger forecasting error. The Bayes-referenced analysis, however, reveals two reversals in this interpretation. First, observed contraction does not imply excessive contraction: sample-wise contrasts generally favor further attenuation, while temporal contrasts span both excessive- and insufficient-contraction regimes. Second, these aggregate tendencies themselves conceal heterogeneous window-level regimes. Within the same model–dataset pair, some windows favor attenuation while others favor amplification, and, in both regimes, larger departures from unit scaling tend to accompany higher error. A contrast-error decomposition further shows that optimal uniform rescaling captures only part of the pooled contrast error, motivating a finer analysis of alignment and window-level heterogeneity. Overall, our results establish a Bayes-referenced view of predictive contraction that distinguishes over-smoothing from uncertainty-induced attenuation and reveals heterogeneous scaling behavior across individual forecasts.