Probabilistic combination forecasts based on particle filtering: predictive prior

2025-08-09

AI Summary

This paper addresses the challenges of inaccurate time-varying ensemble weight estimation and poor multi-step forecasting performance under model misspecification. We propose a Bayesian dynamic ensemble forecasting framework. Methodologically, it introduces a prediction prior driven by model diversity, coupled with a nonlinear state-space model and sequential Monte Carlo (particle filter) inference to enable real-time, adaptive updating of ensemble weights. The proposed prior automatically detects model redundancy, amplifies contributions from informative models, and provides diagnostic capabilities for model incompleteness and predictive uncertainty. Empirical evaluations on oil price forecasting and joint U.S. inflation–GDP forecasting demonstrate that our approach significantly outperforms equal-weight averaging, Bayesian model averaging, and conventional time-varying weighting methods. These results validate its robustness and superiority in complex, nonstationary environments.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Develops Bayesian framework for time-varying forecast weights
• Uses model diversity to improve forecast accuracy
• Applies method to oil price and economic forecasts

Innovation

• Bayesian framework with predictive prior
• Diversity-driven time-varying weights (DTVW)
• Particle filtering in nonlinear state space