Distance and prediction error variance constraints for ARMA model portfolios

Poskitt and Tremayne present a posterior odds ratio (ℜ) portfolio selection strategy for ARMA models. This paper makes the range of prediction error variances that are implicit in ℜ more explicit. Model closeness is quantified using a distance function in a Hilbert space. The relationship between distance and the posterior odds ratio is demonstrated. This provides a distance interpretation of the posterior odds ratio. The distance function also makes it possible to develop a prediction error variance (p.e.v.) criterion for identifying models to include in an ARMA model portfolio. A simulation experiment shows that the p.e.v. criterion provides forecasters with both a measure for assessing the likelihood that the models in an ARMA model portfolio yield practically equivalent forecasts, and a measure for assessing the usefulness of alternative criteria for identifying the order of an ARMA model.