PRISM: A Hierarchical Multiscale Approach for Time Series Forecasting

Time-series forecasting requires identifying which components of the observed context are informative about the future. Multiscale decompositions expose temporal and spectral structure of time series but the predictive relevance of these components can vary across samples and within the context window. We introduce PRISM, a forecasting framework that learns input-dependent selection over localized time-frequency supports of the context window. PRISM constructs a hierarchy of overlapping temporal regions and uses probabilistic selection to couple frequency weighting within each region with band-specific routing between sibling regions. The resulting allocation is learned end-to-end through the forecasting objective. Across eight standard long-horizon benchmarks, PRISM achieves the lowest mean squared error in 20 of 32 settings, and in 61 of 97 settings on GIFT-Eval. Controlled ablations establish the contribution of coupled hierarchical selection beyond flat aggregation and dense mixing. The learned allocations concentrate on a subset of supports, prioritize components whose deletion substantially impairs forecasting, and shift when predictive structure is relocated in synthetic experiments. These results support structured predictive-support selection as an effective inductive bias for time-series forecasting.