Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting

Abstract

We present new methodology and a case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the foundational BPS framework to the multivariate setting, with detailed application in the topical and challenging context of multistep 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 for multiple time series, and—critically—their time-varying inter-dependencies. We define BPS methodology for a new class of 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 U.S. 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.

Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

KEYWORDS:

• Agent opinion analysis
• Bayesian forecasting
• Dynamic latent factors models
• Dynamic SURE models
• Macroeconomic forecasting
• Multivariate density forecast combination

Supplementary Materials

Appendix A provides a summary of MCMC for dynamic BPS. Appendix B provides additional graphical summaries from macroeconomic analysis.

Acknowledgments

This article should not be reported as representing the views of Norges Bank or of the Bank of Japan. The views expressed are those of the authors and do not necessarily reflect those of the Norges Bank or of the Bank of Japan. The authors gratefully acknowledge comments and suggestions from the editor, associate editor, and two anonymous referees. This article is part of the research activities at the Centre for Applied Macro and Petroleum economics (CAMP) at the BI Norwegian Business School. Components of this research were developed while K. McAlinn held a postdoctoral appointment in Econometrics and Statistics at the Booth School of Business, University of Chicago, and while J. Nakajima was at the Monetary and Economic Department, Bank for International Settlements (BIS), Basel.