Distance and prediction error variance constraints for ARMA model portfolios

• Published in: International journal of forecasting 2004, Vol.20 (1), p.41-52
• Main Authors: Chenoweth, Timothy, Dowling, Karen, Hubata, Robert, St. Louis, Robert
• Format: Article
• Language: English
• Subjects: Distance; Forecasting techniques; Information criteria; Misspecification error; Order determination; Posterior odds ratio; Prediction error variance; Studies
• ISSN: 0169-2070; 1872-8200
• DOI: 10.1016/S0169-2070(03)00006-2

Poskitt and Tremayne 74 (1987) 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.