Perspectives on Constrained Forecasting

TL;DR

This paper explores Bayesian decision analysis for constrained forecasting, contrasting it with traditional methods, and introduces novel methodologies for ensuring predictive distributions meet specified constraints, with applications in economic forecasting.

Contribution

It presents new constrained point forecasting and entropic tilting methods, emphasizing decision analysis over traditional inferential approaches in constrained forecasting contexts.

Findings

Development of novel constrained forecasting methodologies

Analysis of the impact of different loss functions on constrained forecasts

Discussion on the role of dependencies among outcomes in 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.