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Bayesian Nonparametric Calibration and Combination of Predictive Distributions

Roberto Casarin (), Federico Bassetti and Francesco Ravazzolo ()
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Federico Bassetti: Department of Mathematics, University of Pavia

No 2015:04, Working Papers from Department of Economics, University of Venice "Ca' Foscari"

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 to account 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. (search for similar items in EconPapers)
JEL-codes: C13 C14 C51 C53 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-for
Date: 2015
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