Non-stationary time series challenge conventional forecasting systems, as their underlying distributions drift, fluctuate, and reorganize over time. To address this, we propose an adaptive modeling framework that interprets temporal evolution through a soft and uncertainty-aware lens. The method embeds each observation into fuzzy membership representations, allowing the system to quantify local deviations from learned temporal patterns. These memberships are integrated through a Bayesian belief propagation mechanism, which stabilizes predictions by recursively tracking evolving temporal structures. An entropy-driven adaptation strategy further modulates update strength, enabling the model to react promptly to genuine regime shifts while avoiding overfitting to transient noise. Evaluated on multiple non-stationary datasets, the proposed framework consistently improves predictive coherence, reduces drift-induced variance, and enhances robustness under shifting dynamics. The results demonstrate that explicitly modeling distributional ambiguity-rather than assuming stationarity-provides a principled pathway for reliable forecasting in dynamic real-world environments.
Zhao et al. (2026) studied this question.