FinHorizon: Persistent Financial Dynamics from Short Windows to Long Paths

The order of daily returns determines how losses cluster and drawdowns unfold. Financial scenario generation therefore requires temporal fidelity throughout long paths, even when learning from short windows. We introduce FinHorizon, a compact neural generator that learns on 128-day windows and produces 512-day financial paths. Its key design is an explicit persistent input: stationary memory states carry latent shocks into nonlinear return dynamics, while a separate Scale Factor calibrates return magnitude after training. Across three evaluation equity indices, FinHorizon achieves the lowest mean Dependence discrepancy among nine benchmark methods at 120, 252, and 512 days, with a 23.0% reduction relative to the strongest benchmark baseline at 512 days. Equal-length segments at the beginning, middle, and end of each rollout retain this benchmark lead, showing that the advantage extends throughout the long path. A paired intervention quantifies the contribution of persistent input: retaining memory reduces 512-day Dependence discrepancy by 31.1% relative to a white-noise input control. These results show how explicit persistence supports temporal fidelity in financial scenarios well beyond the training-window length.