Optimal Prediction Under Asymmetric Loss
研究了非对称损失函数下最优预测的理论问题，推导了可解析求解情况下的最优预测器，并指出最优预测存在时变偏差，依赖于高阶条件矩，例如波动率动态（如GARCH效应）会影响最优点预测。
Prediction problems involving asymmetric loss functions arise routinely in many fields, yet the theory of optimal prediction under asymmetric 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 under asymmetric loss and that the conditionally optimal amount of bias is time varying in general and depends on higher order conditional moments. Thus, for example, volatility dynamics (e.g., GARCH effects) are relevant for optimal point prediction under asymmetric loss. More generally, even for models with linear conditionalmean structure, the optimal point predictor is in general nonlinear under asymmetric loss, which provides a link with the broader nonlinear time series literature.