By Jiahao Weng, Jiyu Liu
Time-series observations are particularly susceptible to noise, and many real-world series have low signal-to-noise ratios (SNRs) together with heavy-tailed and time-varying disturbances. When Gaussian diffusion models are used for forecasting, reversing all the way to the zero-noise endpoint may yield an overly narrow and overconfident predictive distribution. We propose SHADE, an alpha-stable Lévy diffusion forecaster that reads out at a nonzero depth so that the residual stable kernel acts as distribution-level shrinkage. By decomposing halting risk into smoothing bias and estimation error, we develop a scale-calibrated halt for estimating the optimal shrinkage τ^* and a context-amortized halt that requires no explicit noise labels. Gains concentrate in the extreme heavy-tailed regime α≤1.3: Across synthetic noise settings, median CRPS improves by 21.7%, while the NLL falls significantly; Cryptocurrency and foreign-exchange data provide further evidence of improved tail calibration in real-data implement. On near-light-tailed or high-SNR data, the model reverts to Gaussian diffusion or full denoising. SHADE maintains overall forecast error comparable to strong baselines while providing more honest tail uncertainty for heavy-tailed series.
The interactive Everscope explorer (charts, battles, favorites) loads below.