Dynamic Bayesian regression quantile synthesis for forecasting outlook-at-risk

2026-03-11

AI Summary

This study addresses the limitation of existing Bayesian predictive synthesis methods, which primarily focus on mean forecasting and struggle to effectively integrate quantile information from multiple models to characterize risk profiles. The work proposes a novel extension of Bayesian predictive synthesis to the quantile forecasting domain, introducing a dynamic quantile linear model and its multivariate factor-augmented variant. By directly modeling conditional quantiles via the asymmetric Laplace distribution and incorporating time-varying latent factors to capture dynamic cross-sectional dependencies, the framework enables adaptive weight adjustment through an efficient MCMC algorithm based on data augmentation and forward-filtering backward-sampling. Empirical results demonstrate superior predictive performance in forecasting U.S. inflation and global GDP growth, with notable robustness and accuracy during extreme economic shocks such as the COVID-19 pandemic.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

This paper proposes dynamic Bayesian regression quantile synthesis (DRQS), a novel method for quantile forecasting within the Bayesian predictive synthesis (BPS) framework designed to combine quantile-specific information from multiple agent models. While existing BPS approaches primarily focus on mean forecasting, our method directly targets the conditional quantiles of the response variable by utilizing the asymmetric Laplace distribution for the synthesis function. The resulting framework can be interpreted as a dynamic quantile linear model with latent predictors. We extend the univariate DRQS to a multivariate setting-factor DRQS (FDRQS)-by introducing a time-varying latent factor structure for the synthesis weights. This allows the model to leverage cross-sectional dependencies and shared information across multiple time series simultaneously. We develop an efficient Markov chain Monte Carlo (MCMC) algorithm for posterior inference, utilizing data augmentation and forward-filtering backward-sampling. Empirical applications to US inflation and global GDP growth demonstrate the improved performance of the proposed methods for quantile forecasting. In particular, FDRQS exhibits superior resilience during periods of extreme economic stress, such as the COVID-19 pandemic, by adaptively rebalancing agent contributions and capturing emergent global dependencies.

Problem

• quantile forecasting
• Bayesian predictive synthesis
• conditional quantiles
• multivariate time series
• extreme economic stress

Innovation

• Dynamic Bayesian regression quantile synthesis
• Bayesian predictive synthesis
• Quantile forecasting
• Time-varying latent factors
• Asymmetric Laplace distribution