A Bayesian Nonlinear Forecast Combination Method

• Activity Number: 490
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Kajal Lahiri*+ and Yang Liu
• Companies: SUNY Albany and SUNY Albany
• Keywords: ROC curve ; Recessions ; Copulas ; Bayesian Analysis ; MCMC ; Survey forecasts

Abstract

We develop a non-linear forecast combination procedure for turning point predictions based on t-copulas that incorporates the dynamic interactions between individual predictors across regimes. This approach is optimal in the sense that the resulting combined forecast produces the highest discriminatory power as measured by the Receiver Operating Characteristic (ROC) curve. Under certain conditions, this rule is shown to be equivalent to the linear combination scheme suggested by Bates and Granger (Operation Research Quarterly, 1969). Following Muller (Econometrica, 2013) we develop our approach based on robust marginal distributions. We implement our procedure to revisit a puzzle initially established by Rudebusch and Williams (JBES, 2009). We optimally combine yield spread and SPF probability forecasts for real GDP declines, and examine the sources of forecasting gains at different horizons using a counterfactual experimental set up. We decompose the overall improvement of the combined forecast relative to each predictor into gains from i) recalibration, ii) using the differentials in copulas between regimes, and iii) using the differentials in the alternative predictor.