🤖 AI Summary
This work addresses the issue of quantile crossing and inconsistency with candlestick geometric structure in probabilistic candlestick forecasting. To resolve this, we propose the K-line–Quantile Sequential Projection (KQSP) method, a post-processing technique that enforces strict quantile monotonicity and candlestick shape constraints on probabilistic predictions from any pretrained model—without requiring architectural modifications or retraining. KQSP employs a parameter-free, training-agnostic sequential projection algorithm, uniquely eliminating both types of crossing simultaneously for the first time. Experimental results demonstrate that KQSP reduces both quantile crossing rates and candlestick crossing rates to zero across all test datasets, achieving these guarantees with significantly smaller correction magnitudes compared to existing approaches, while preserving the original forecast accuracy.
📝 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.