Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2017, Volume 85, Issue 2

Forecasting with Model Uncertainty: Representations and Risk Reduction
p. 617-643

Keisuke Hirano, Jonathan H. Wright

We consider forecasting with uncertainty about the choice of predictor variables. The researcher wants to select a model, estimate the parameters, and use the parameter estimates for forecasting. We investigate the distributional properties of a number of different schemes for model choice and parameter estimation, including: in‐sample model selection using the Akaike information criterion; out‐of‐sample model selection; and splitting the data into subsamples for model selection and parameter estimation. Using a weak‐predictor local asymptotic scheme, we provide a representation result that facilitates comparison of the distributional properties of the procedures and their associated forecast risks. This representation isolates the source of inefficiency in some of these procedures. We develop a simulation procedure that improves the accuracy of the out‐of‐sample and split‐sample methods uniformly over the local parameter space. We also examine how bootstrap aggregation (bagging) affects the local asymptotic risk of the estimators and their associated forecasts. Numerically, we find that for many values of the local parameter, the out‐of‐sample and split‐sample schemes perform poorly if implemented in the conventional way. But they perform well, if implemented in conjunction with our risk‐reduction method or bagging.

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Supplemental Material

Supplement to "Forecasting with Model Uncertainty: Representations and Risk Reduction"

This zip file contains the replication files for the manuscript.

Supplement to "Forecasting with Model Uncertainty: Representations and Risk Reduction"

This supplementary material introduces some alternative procedures to the ones considered in the main text, and provides extended numerical comparisons of local asymptotic risk among the various methods. It also conducts a small Monte Carlo study of finite-sample risk, and provides a comparison of shrinkage factors for a number of the procedures.