Threshold Martingales and the Evolution of Forecasts
阈值鞅与预测分布的演化
This paper introduces a martingale that characterizes two properties of evolving forecast distributions. Ideal forecasts of a future event behave as martingales, sequen- tially updating the forecast to leverage the available information as the future event approaches. The threshold martingale introduced here measures the proportion of the forecast distribution lying below a threshold. In addition to being calibrated, a threshold martingale has quadratic variation that…