“…Although ξ = 0.5 is a natural threshold in equation (), it is not a fully objective selection, because the success ratios and market timing tests are highly dependent on the selected threshold. Therefore, we also look at an alternative approach to assess the accuracy of probability forecasts, namely the receiver operating characteristic (ROC) curve, which has recently been used in a growing number of economic applications (see, for example, Berge and Jorda , Schularick and Taylor , Lahiri and Wang , Christiansen et al, ). The ROC curve is a mapping of the true positive rate: and the false positive rate: for all possible thresholds 0≤ ξ ≤1, described as an increasing function in [0,1] × [0,1] space, with TP( ξ ) plotted on the y ‐axis and FP|( ξ ) on the x ‐axis.…”