An example of an optimal forecast exhibiting decreasing bias with increasing forecast horizon

Aretz, Kevin and Peel, David (2013) An example of an optimal forecast exhibiting decreasing bias with increasing forecast horizon. Bulletin of Economic Research, 65 (4). pp. 362-371. ISSN 0307-3378

Abstract

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.