Crossing-Free Probabilistic K-Line Forecasts Without Retraining

The paper proposes K-line–Quantile Sequential Projection (KQSP), a parameter-free and training-free reconciliation method for probabilistic OHLC forecasts. It addresses both quantile crossing and K-line crossing, where predicted quantiles violate ordering or predicted highs and lows become inconsistent with open and close prices. KQSP can be applied to outputs from any forecasting model, including pretrained foundation models. According to the abstract, it reduces both crossing rates to zero on all evaluated test data while preserving predictive accuracy and making smaller corrections than competing crossing-resolution methods.