Forecasting With Model Uncertainty: Representations and Risk Reduction
研究了预测变量选择不确定时，不同模型选择与参数估计方案的分布性质，提出了一种能统一改进样本外和分割样本方法预测精度的模拟程序。
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: in-sample model selection using the Akaike information criterion, out-ofsample 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. 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.