Bayesian Nonparametric Calibration and Combination of Predictive Distributions. Issue 522 (3rd April 2018)

• Record Type: Journal Article
• Authors: Bassetti, Federico; Casarin, Roberto; Ravazzolo, Francesco
• Is Part Of: Journal of the American Statistical Association. Volume 113:Issue 522(2018)
• Page Start: 675
• Page End: 685
• Publication Date: 2018-04-03
• Subjects: Bayesian nonparametrics -- Density forecast -- Forecast calibration -- Forecast combination -- Posterior consistency; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2016.1273117
• Languages: English
• ISSNs: 0162-1459

Abstract

ABSTRACT: We introduce a Bayesian approach to predictive density calibration and combination that accounts for parameter uncertainty and model set incompleteness through the use of random calibration functionals and random combination weights. Building on the work of Ranjan and Gneiting, we use infinite beta mixtures for the calibration. The proposed Bayesian nonparametric approach takes advantage of the flexibility of Dirichlet process mixtures to achieve any continuous deformation of linearly combined predictive distributions. The inference procedure is based on combination Gibbs and slice sampling. We provide some conditions under which the proposed probabilistic calibration converges in terms of weak posterior consistency to the true underlying density for both cases of iid and Markovian observations. This calibration property improves upon the earlier calibration approaches. We study the methodology in simulation examples with fat tails and multimodal densities and apply it to density forecasts of daily S&P returns and daily maximum wind speed at the Frankfurt airport. Supplementary materials for this article are available online.