OPTIMAL PREDICTION UNDER ASYMMETRIC LOSS

Prediction problems involving asymmetric loss functions arise routinel y in many fields, yet the theory of optimal prediction under asymmetri c loss is not well developed. We study the optimal prediction problem under general loss structures and characterize the optimal predictor, We compute the optimal predictor analytically in two leading tractable cases and show how to compute it numerically in less tractable cases. A key theme is that the conditionally optimal forecast is biased unde r asymmetric loss and that the conditionally optimal amount of bias is time varying in general and depends on higher order conditional momen ts. Thus, for example, volatility dynamics (e.g., GARCH effects) are r elevant for optimal point prediction under asymmetric loss, More gener ally, even for models with linear conditional-mean structure, the opti mal point predictor is in general nonlinear under asymmetric loss, whi ch provides a link with the broader nonlinear time series literature.