Conditional Projective Scenario Systems for Long-Horizon Joint Forecasting

Modern time-series foundation models (TSFMs) can estimate value distributions at individual future time steps, but these marginals do not specify which values are likely to occur together. This matters for quantities such as the future maximum, maximum one-step change, or time spent above a threshold, which depend on the complete forecast trajectory. In this study, we introduce the Conditional Projective Scenario System (CPSS), which transforms marginal forecasts from a frozen TSFM (TimesFM-2.5) into 64 weighted complete trajectories. CPSS first represents broad future alternatives and then introduces finer variations while preserving consistency across forecast horizons, so identical truncated prefixes are merged and their probabilities summed. Across eight datasets, CPSS achieves increasing gains over a closely matched 64-trajectory baseline as the forecast horizon grows. On a separate 12-domain, 128-step benchmark, CPSS reduces complete-trajectory error by 6.80% and error on path-dependent quantities by 16.80%. Under present evidence, these results demonstrate that CPSS can extend strong marginal forecasters into coherent scenario generators, showing great promise for more accurate probabilistic reasoning over complete future trajectories.