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Abstract
Decision-makers often consult different experts to build reliable forecasts on variables of interest. Combining more opinions and calibrating them to maximize the forecast accuracy is consequently a crucial issue in several economic problems. This paper applies a Bayesian beta mixture model to derive a combined and calibrated density function using random calibration functionals and random combination weights. In particular, it compares the application of linear, harmonic and logarithmic pooling in the Bayesian combination approach. The three combination schemes, i.e., linear, harmonic and logarithmic, are studied in simulation examples with multimodal densities and an empirical application with a large database of stock data. All of the experiments show that in a beta mixture calibration framework, the three combination schemes are substantially equivalent, achieving calibration, and no clear preference for one of them appears. The financial application shows that the linear pooling together with beta mixture calibration achieves the best results in terms of calibrated forecast.
Highlights
IntroductionDecision-makers often consult experts for reliable forecast about some uncertain future outcomes
Decision-makers often consult experts for reliable forecast about some uncertain future outcomes.Expert opinion has been used in a more or less systematic way in many fields: weather forecast, aerospace programs, military intelligence, nuclear energy and in policy analysis
Among the first papers on forecasting with more predictions, we refer to Barnard [1], who considered air passenger data, and Roberts [2], who introduced a distribution that is essentially a weighted average of the posterior distributions of two models and is similar to the result of a Bayesian model averaging (BMA)
Summary
Decision-makers often consult experts for reliable forecast about some uncertain future outcomes. Linear pooling, proposed by Stone [11], has been used almost exclusively in empirical applications on the density forecast combination; see [12,13]. Extending [15,20], they propose both finite beta and infinite beta mixtures for the calibration For the combination, they apply a local linear pool. We apply a beta mixture approach to combine and calibrate prediction functions and compare linear, harmonic and logarithmic pooling in the application of the Bayesian approach. Relative to [19], we keep the number of beta components fixed to achieve calibration of the combination, but extend their methodology to the family of generalized linear combination schemes (i.e., harmonic and logarithmic) proposed in [12].
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