Forecasting Nonlinear Functions of Returns Using LINEX Loss Functions

This paper applies LINEX loss functions to forecasting nonlinear functions of variance. We derive the optimal one-step-ahead LINEX forecast for various volatility models using data transformations such as ln(y2t) where yt is the return of the asset. Our results suggest that the LINEX loss function is particularly well-suited to many of these forecasting problems and can give better forecasts than conventional loss functions such as mean square error (MSE).