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

Genya Kobayashi, Shonosuke Sugasawa, Yuta Yamauchi, Dongu Han

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.

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

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.
Paper Structure (25 sections, 20 equations, 24 figures, 2 tables)

This paper contains 25 sections, 20 equations, 24 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Dynamic regression quantile synthesis
  3. Bayesian predictive synthesis
  4. DRQS for single time series
  5. Forecasting quantiles with DRQS
  6. Forecasting US inflation-at-risk
  7. Factor DRQS for multiple time series
  8. Forecasting global growth-at-risk
  9. Data and setting
  10. Result
  11. Quantile forecasting performance
  12. Parameter estimates
  13. Predictive distributions of growth rates
  14. Concluding remarks
  15. Acknowledgements
  16. ...and 10 more sections

Figures (24)

  • Figure 1: Cumulative CRPS relative to DQLM1 for $h=1$ (top panels) and $h=4$ (bottom panels).
  • Figure 2: One-step ahead predictive means (solid lines) and 95% intervals (shaded areas) of $0.1$th, $0.5$th and $0.9$th quantiles under DRQS, DQLM2 and DQLM4 for $h=1$ (top panels) and $h=4$ (bottom panels). Points indicate the observed inflation rates.
  • Figure 3: Annualised quarterly growth rates ($h=1$) of the eighteen countries divided by the regions.
  • Figure 4: Time series plots of the cumulative total CRPS relative to FQBART.
  • Figure 5: Time series plots of the cumulative CRPS with none relative to FQBART for each contry ($h=1$).
  • ...and 19 more figures