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Bayesian Nonparametric Calibration and Combination of Predictive Distributions

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Version 2 2018-02-23, 20:45
Version 1 2017-01-05, 21:33
journal contribution
posted on 2018-02-23, 20:45 authored by Federico Bassetti, Roberto Casarin, Francesco Ravazzolo

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.

Funding

Casarin's research is supported by funding from the European Union, Seventh Framework Programme FP7/2007-2013 under grant agreement SYRTO-SSH-2012-320270, by the Institut Europlace of Finance, “Systemic Risk grant,” the Global Risk Institute in Financial Services, the Louis Bachelier Institute, “Systemic Risk Research Initiative,” and by the Italian Ministry of Education, University and Research (MIUR) PRIN 2010-11 grant MISURA. Bassetti's research is supported by the INdAm-GNAMPA Project 2016, and by the Italian Ministry of Education, University and Research (MIUR), PRIN 2015 grant “Modern Bayesian nonparametric methods”. This research used the SCSCF multiprocessor cluster system at University Ca’ Foscari of Venice.

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