Forecasting with Model Uncertainty: Representations and Risk Reduction∗

We consider forecasting with uncertainty about the choice of predictor variables. The researcher wants to select a model, estimate the parameters, and use this for forecasting. We investigate the distributional properties of a number of different schemes for model choice and parameter estimation: 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 weakpredictor local asymptotic scheme, we provide a representation result that facilitates comparison of the distributional properties of the procedures and their associated forecast risks. 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. ∗We are grateful to Don Andrews, Marine Carrasco, Russell Davidson, Gary Chamberlain, Sylvia Gonçalves, Bruce Hansen, Serena Ng, Peter Phillips, and Jack Porter for very helpful discussions. The usual disclaimer applies. †Department of Economics, University of Arizona, 1130 E. Helen St., Tucson AZ 85721. Email: [email protected] ‡Department of Economics, Johns Hopkins University, 3400 North Charles St., Baltimore MD 21218. Email: [email protected] 1