AN EXAMPLE OF AN OPTIMAL FORECAST EXHIBITING DECREASING BIAS WITH INCREASING FORECAST HORIZON

Motivated by a central banker with an inflation target, we show that the optimal forecast bias under non-quadratic loss functions and non-normal forecast errors can decrease or initially increase and then decrease with the forecast horizon. We initially proof that, if the variable to forecast can be described by a generalized Rayleigh distribution, its conditional mean does in general not constitute the optimal prediction under a symmetric target zone loss function. Subsequently, we approximate the target zone loss function to show the potential for variation in optimal bias over the forecast horizon.