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

TL;DR

This paper introduces a dynamic Bayesian regression quantile synthesis method that combines multiple models for improved quantile forecasting, especially during economic stress, by leveraging latent factors and Bayesian inference.

Contribution

It develops a novel Bayesian framework for quantile forecasting that extends to multivariate settings with latent factors, enhancing predictive accuracy during crises.

Findings

FDRQS outperforms existing methods in forecasting US inflation and global GDP.

The model demonstrates robustness during COVID-19 economic stress periods.

Efficient MCMC algorithms enable practical implementation of the complex model.

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.