Bayesian Reconciliation of Overlapping Multi-Step Forecasts: A Post-Processing Framework for Cross-Origin Coherence
Multi-step forecasting systems, including modern artificial intelligence (AI) models, often issue overlapping predictions for the same future time from different forecast origins. These predictions can disagree even when produced by the same model, a phenomenon we call cross-origin incoherence. We propose a Bayesian reconciliation framework that treats overlapping forecasts as noisy and potentially biased measurements of a common latent trajectory. The method operates as a model agnostic post-processing layer, requiring no access to the forecasting models architecture, parameters, or training data. A Bayesian state-space model jointly reconciles forecasts targeting the same future time while accounting for horizon-specific bias and uncertainty. Controlled simulations demonstrate substantial reductions in cross-origin incoherence and accurate latent trajectory recovery under the assumed data generating process. An empirical application to daily S and P 500 volatility forecasts reduces 90% prediction interval coverage from 94.8% to 88.3%, closer to nominal coverage, but increases point forecast error. An additional LSTM experiment demonstrates applicability to modern neural forecasting systems.