Bayesian Nonparametric Calibration and Combination of Predictive Distributions

47 Pages Posted: 4 May 2015

See all articles by Federico Bassetti

Federico Bassetti

University of Pavia

Roberto Casarin

University Ca' Foscari of Venice - Department of Economics

Francesco Ravazzolo

Free University of Bozen-Bolzano - Faculty of Economics and Management; BI Norwegian Business School

Multiple version iconThere are 2 versions of this paper

Date Written: February 25, 2015

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 (2010) and Gneiting and Ranjan (2013), 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 Gibbs sampling and allows accounting for uncertainty in the number of mixture components, mixture weights, and calibration parameters. The weak posterior consistency of the Bayesian nonparametric calibration is provided under suitable conditions for unknown true density. 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.

Keywords: Forecast calibration, Forecast combination, Density forecast, Beta mixtures, Bayesian nonparametrics, Slice sampling

JEL Classification: C13, C14, C51, C53

Suggested Citation

Bassetti, Federico and Casarin, Roberto and Ravazzolo, Francesco, Bayesian Nonparametric Calibration and Combination of Predictive Distributions (February 25, 2015). Norges Bank Working Paper 3 | 2015. Available at SSRN: https://ssrn.com/abstract=2602465 or http://dx.doi.org/10.2139/ssrn.2602465

Federico Bassetti (Contact Author)

University of Pavia ( email )

Corso Strada Nuova, 65
27100 Pavia, 27100
Italy

Roberto Casarin

University Ca' Foscari of Venice - Department of Economics ( email )

San Giobbe 873/b
Venice, 30121
Italy
+39 030.298.91.49 (Phone)
+39 030.298.88.37 (Fax)

HOME PAGE: http://venus.unive.it/r.casarin/

Francesco Ravazzolo

Free University of Bozen-Bolzano - Faculty of Economics and Management ( email )

Via Sernesi 1
39100 Bozen-Bolzano (BZ), Bozen 39100
Italy

BI Norwegian Business School ( email )

Nydalsveien 37
Oslo, 0442
Norway

HOME PAGE: http://www.francescoravazzolo.com/

Register to save articles to
your library

Register

Paper statistics

Downloads
32
Abstract Views
264
PlumX Metrics