Probabilistic Indicator Lifting, Copula Sensitivity, and Multi-Scale Interference in Deep-Learning Financial Forecasting

We establish Forecast Horizon Analytics (FHA) to support multi-step financial decision-making under probabilistic forecasts. A pushforward horizon lift distinguishes quantities identified by marginal forecasts from those requiring joint path laws. We characterize expected occupation measures, sharp barrier probability bounds, and Monte Carlo error under model discrepancy. Across multi-scale timeframes, we develop continuous variance-clock conditioning and stock-variable trace reconciliation (MinT). Finally, we demonstrate that passive limit orders suffer conditional adverse selection and formulate a validation harness with HAC asymptotics, Christoffersen conditional coverage tests, and Romano–Wolf multiple-testing control.