Forecasting Nonlinear Functions of Returns Using LINEX Loss Functions

Soosung Hwang

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 $ln(y_{t}^{2})$ where $% y_{t}$ 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).