Threshold-Consistent Learning for Continuous Forecasting and Rare-Event Detection

Continuous forecasting and rare-event detection are often treated as separate objectives in financial time-series forecasting, although they describe two aspects of the same future outcome. A regression model may achieve low prediction error while assigning insufficiently high scores to rare but decision-critical events, such as unusually large positive returns. We propose Threshold-Consistent Continuous–Discrete Learning (TCDL), a unified framework that jointly learns continuous return prediction and threshold-defined event states. The key idea is to couple the continuous prediction with a discrete state representation through a threshold-consistency objective, encouraging the predicted return and inferred event state to remain logically aligned during optimization. In this way, the continuous task preserves fine-grained numerical information, while the discrete task improves sensitivity to rare tail events. We evaluate TCDL across major global market indices against strong time-series forecasting baselines. The proposed method maintains strong regression accuracy while achieving competitive rare-event discrimination and substantially improving tail AUPRC over conventional regression and joint-learning objectives. Statistical significance tests and controlled ablations further isolate the contribution of the threshold-consistency mechanism. These results show that coupling continuous predictions with threshold-defined decision states provides a simple and effective learning paradigm for forecasting problems in which rare events are more consequential than average prediction error.