Forecasting using belief functions: An application to marketing econometrics

•A method is proposed to quantify forecast uncertainty using belief functions.•The method is simple and can be applied to any parametric statistical model.•The approach does not require to specify a prior distribution on the parameter.•The Bayesian approach is recovered as a special case when a prior is provided.•The method is applied to innovation diffusion forecasting using the Bass model.

A method is proposed to quantify uncertainty on statistical forecasts using the formalism of belief functions. The approach is based on two steps. In the estimation step, a belief function on the parameter space is constructed from the normalized likelihood given the observed data. In the prediction step, the variable Y to be forecasted is written as a function of the parameter θ and an auxiliary random variable Z with known distribution not depending on the parameter, a model initially proposed by Dempster for statistical inference. Propagating beliefs about θ and Z through this model yields a predictive belief function on Y. The method is demonstrated on the problem of forecasting innovation diffusion using the Bass model, yielding a belief function on the number of adopters of an innovation in some future time period, based on past adoption data.