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This paper introduces K-line-Quantile Sequential Projection (KQSP), a novel method that addresses both quantile and K-line crossing issues in probabilistic K-line forecasting without the need for retraining. By applying KQSP, the authors demonstrate that it is possible to achieve zero crossing rates while maintaining predictive accuracy across various models, including pretrained foundation models. The findings highlight that KQSP can effectively reconcile forecast inconsistencies in a parameter-free manner, marking a significant advancement in probabilistic forecasting techniques.
KQSP eliminates forecast crossing issues without retraining, achieving zero crossing rates while preserving accuracy across diverse models.
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.
