Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting

TL;DR

This paper introduces a multivariate Bayesian predictive synthesis framework for macroeconomic forecasting, enabling adaptive evaluation of forecast biases, miscalibration, and interdependencies among multiple economic time series over time.

Contribution

It extends Bayesian predictive synthesis to multivariate settings with new methodology for dynamic latent factor models, applied to multi-step macroeconomic forecasting.

Findings

BPS improves forecast accuracy across multiple series and horizons.

It reveals dynamic relationships among forecasting models.

The approach adapts to changing biases and dependencies over time.

Abstract

We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the multivariate setting, with detailed application in the topical and challenging context of multi-step macroeconomic forecasting in a monetary policy setting. BPS evaluates-- sequentially and adaptively over time-- varying forecast biases and facets of miscalibration of individual forecast densities, and-- critically-- of time-varying inter-dependencies among them over multiple series. We develop new BPS methodology for a specific subclass of the dynamic multivariate latent factor models implied by BPS theory. Structured dynamic latent factor BPS is here motivated by the application context-- sequential forecasting of multiple US macroeconomic time series with forecasts generated from several traditional econometric time series models. The case study highlights the potential of BPS to improve of forecasts of multiple series at multiple forecast horizons, and its use in learning dynamic relationships among forecasting models or agents.