Directional Prediction of Returns under Asymmetric Loss: Direct and Indirect Approaches

To predict a return characteristic, one may construct models of different complexity describing the dynamics of different objects. The most complex object is the entire predictive density, while the least complex is the characteristic whose forecast is of interest. This paper investigates, using experiments with real data, the relation between the complexity of the modeled object and the predictive quality of the return characteristic of interest, in the case when this characteristic is a return sign, or, equivalently, the direction-of-change. Importantly, we carry out the comparisons assuming that the underlying loss function is asymmetric, which is more plausible than the quadratic loss still prevailing in the analysis of returns. Our experiments are performed with returns of various frequencies on a stock market index and exchange rate. By and large, modeling the dynamics of returns by autoregressive conditional quantiles tends to produce forecasts of higher quality than modeling the whole predictive density or modeling the return indicators themselves.