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This research introduces KQSP, a post-processing method that enforces logical consistency in probabilistic financial forecasts without requiring model retraining. By resolving quantile and price-level crossing issues across various architectures including foundation models, the technique preserves predictive accuracy while eliminating data integrity errors inherent to standard uncertainty estimation.
Crossing-Free Probabilistic K-Line Forecasts Without Retraining
arXiv:2607.26792v1 Announce Type: cross Abstract: Probabilistic K-line forecasting describes uncertainty in four complementary prices, namely open--high--low--close (OHLC). However, it introduces two consistency problems: quantile crossing and K-line crossing. Quantile crossing occurs when a higher-quantile forecast falls below a lower-quantile forecast, while K-line crossing occurs when the forecast low exceeds the open or close, or the forecast high falls below the open or close. Existing solutions generally address only one problem through output reordering, specialized architectures, or penalized training objectives. We propose K-line--Quantile Sequential Projection (KQSP), a parameter-free and training-free reconciliation method applicable to forecasts produced by any model. Compared with other crossing solutions, KQSP preserves predictive accuracy while producing substantially smaller corrections to the original forecasts. To mitigate model bias, we evaluate KQSP using various models, including pretrained foundation models. KQSP reduces both quantile and K-line crossing rates to zero for all test data undertaken. These results show that probabilistic K-line consistency can be enforced independently of forecast generation and without retraining.
Abstract:Probabilistic K-line forecasting describes uncertainty in four complementary prices, namely open--high--low--close (OHLC). However, it introduces two consistency problems: quantile crossing and K-line crossing. Quantile crossing occurs when a higher-quantile forecast falls below a lower-quantile forecast, while K-line crossing occurs when the forecast low exceeds the open or close, or the forecast high falls below the open or close. Existing solutions generally address only one problem through output reordering, specialized architectures, or penalized training objectives. We propose K-line--Quantile Sequential Projection (KQSP), a parameter-free and training-free reconciliation method applicable to forecasts produced by any model. Compared with other crossing solutions, KQSP preserves predictive accuracy while producing substantially smaller corrections to the original forecasts. To mitigate model bias, we evaluate KQSP using various models, including pretrained foundation models. KQSP reduces both quantile and K-line crossing rates to zero for all test data undertaken. These results show that probabilistic K-line consistency can be enforced independently of forecast generation and without retraining.
Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Computational Engineering, Finance, and Science (cs.CE); Machine Learning (cs.LG); Computational Finance (q-fin.CP)
arXiv:2607.26792 [stat.ML]
(or arXiv:2607.26792v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2607.26792 arXiv-issued DOI via DataCite (pending registration)
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