Perspectives on Constrained Forecasting

Abstract

This expository paper discusses Bayesian decision analysis perspectives on problems of constrained forecasting. Foundational and pedagogic discussion contrasts decision analytic approaches with the traditional, but typically inappropriate, inferential approach. Illustrative examples include development of novel constrained point forecasting and entropic tilting methodology to explore consistency of a predictive distribution with an imposed or hypothesized constraint. Linear, aggregate constraints define illuminating examples that relate to broadly important problems involving aggregate and hierarchical constraints in commercial and economic forecasting. Discussion explores the impact of different loss functions, questions of how constrained forecasting is impacted by dependencies among outcomes being predicted, and promotes the broader use of decision analysis including routine evaluation of predictive distributions of loss under chosen forecasts/decisions. Extensions to more general constrained forecasting problems, connections with broader interests in forecast reconciliation and other considerations are noted.