The geometric combination of Bayesian forecasting models

A nonlinear geometric combination of statistical models is proposed as an alternative approach to the usual linear combination or mixture. Contrary to the linear, the geometric model is closed under the regular exponential family of distributions, as we show. As a consequence, the distribution which results from the combination is unimodal and a single location parameter can be chosen for decision making. In the case of Student t-distributions (of particular interest in forecasting) the geometric combination can be unimodal under a sufficient condition we have established. A comparative analysis between the geometric and linear combinations of predictive distributions from three Bayesian regression dynamic linear models, in a case of beer sales forecasting in Zimbabwe, shows the geometric model to consistently outperform its linear counterpart as well as its component models.