FURTHER RESULTS ON FORECASTING AND MODEL SELECTION UNDER ASYMMETRIC LOSS

We make three related contributions. First, we propose a new technique for solving prediction problems under asymmetric loss using piecewise -linear approximations to the loss function, and we establish existenc e and uniqueness of the optimal predictor. Second, we provide a detail ed application to optimal prediction of a conditionally heteroscedasti c process under asymmetric loss, the insights gained from which are br oadly applicable. Finally, we incorporate our results into a general f ramework for recursive prediction-based model selection under the rele vant loss function.