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