Beyond Regression: Probabilistic Ranking for Financial Forecasting

Financial time-series forecasting is commonly formulated as point regression, although minimizing prediction error does not necessarily produce effective ranking or discrimination of rare, decision-relevant movements. We propose a probabilistic market-state forecasting framework that represents both historical patterns and future returns in discrete spaces. Historical OHLC patches are quantized into tokens and encoded by a lightweight causal Transformer, while upward- and downward-oriented target codebooks define future return states predicted through dual classification heads. The probabilities of selected extreme states are aggregated into directional scores for return ranking and tail-event identification. Experiments on ten major equity indices across multiple chronological periods show consistent improvements over regression-based forecasters in rank correlation and the identification of extreme upward and downward movements. Ablation results show that input and target discretization provide complementary benefits. Furthermore, decision-level fusion combines the state probabilities with existing regression forecasts, improving both ranking quality and point-error metrics. These results demonstrate that discrete return-state probabilities capture decision-relevant information that point-regression objectives alone do not adequately represent.