Probabilistic combination forecasts based on particle filtering: predictive prior

Abstract: We develop a Bayesian combination forecast framework that incorporates forward-looking signals as a predictive prior into the estimation of time-varying combination weights, enabling the weights to reflect both historical data and forward-looking information from individual models. Model diversity is employed as a feature to represent forward-looking feedback, giving rise to the proposed method termed diversity time-varying weights (DTVW). The weights are estimated via particle filtering within a nonlinear state space. This method extends the time-varying weights (TVW) by integrating diversity-driven predictive priors, which penalize redundancy and encourage informative contributions across individual models. Simulation studies demonstrate improved forecast accuracy across both simple complete model set and complex misspecified one, with these gains stemming from the framework's ability to dynamically assess the relative performance of individual models and allocate weights accordingly. Empirically, we apply the method to multi-step ahead oil price forecast and bi-variate forecast of U.S. inflation and GDP growth. In both cases, the proposed method DTVW outperforms traditional combination forecasts, such as the Equal Weighting, Bayesian Model Averaging, TVW, etc. Additionally, using model diversity as a predictive prior provides diagnostic insights into model incompleteness and forecast uncertainty in evolving complex economic environments.