Dynamic modeling under linear-exponential loss

We develop a methodology of parametric modeling of time series dynamics when the underlying loss function is linear-exponential (Linex). We propose to directly model the dynamics of the conditional expectation that determines the optimal predictor. The procedure hinges on the exponential quasi-maximum likelihood interpretation of the Linex loss and nicely fits the multiplicative error modeling framework. Many conclusions relating to estimation, inference and forecasting follow from results already available in the econometric literature. The methodology is illustrated using data on United States GNP growth and Treasury bill returns.