Using a Bayesian framework this paper provides a multivariate combination approach to prediction based on a distributional state space representation of predictive densities from alternative models. In the proposed approach the model set can be incomplete. Several multivariate time-varying combination strategies are introduced. In particular, a weight dynamics driven by the past performance of the predictive densities is considered and the use of learning mechanisms. The approach is assessed using statistical and utility-based performance measures for evaluating density forecasts of US macroeconomic time series and of surveys of stock market prices.

Additional Metadata
Keywords Baysian filtering, density forecast combination, sequential Monte Carlo, survey forecast
JEL Bayesian Analysis (jel C11), Simulation Methods; Monte Carlo Methods; Bootstrap Methods (jel C15), Forecasting and Other Model Applications (jel C53), Forecasting and Simulation (jel E37)
Publisher Tinbergen Institute
Persistent URL
Series Tinbergen Institute Discussion Paper Series
Journal Discussion paper / Tinbergen Institute
Billio, M, Casarin, R, Ravazzolo, F, & van Dijk, H.K. (2011). Combining Predictive Densities using Bayesian Filtering with Applications to US Economics Data (No. TI 2011-003/4). Discussion paper / Tinbergen Institute. Tinbergen Institute. Retrieved from