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 existence and uniqueness of the optimal predictor. Second, we provide a detailed application to optimal prediction of a conditionally heteroscedastic process under asymmetric loss, the insights gained from which are broadly applicable. Finally, we incorporate our results into a general framework for recursive prediction-based model selection under the relevant loss function.