Rank-invariance conditions for the comparison of volatility forecasts
推导了四个保证秩不变的条件，即基于有测量误差的方差代理变量的波动率预测排名与基于不可观测条件方差的真实排名一致，并通过蒙特卡洛模拟和矩条件研究了这些条件对预测偏差、方差和相关性等特征的影响。
Summary The paper derives four conditions that guarantee rank-invariance, i.e., that the empirical rankings (based on measurement error-affected variance proxies) of competing volatility forecasts be consistent with the true rankings (based on the unobservable conditional variance). The first three establish bounds beyond which the separation between the forecasts is enough for their rankings not to be affected by the measurement error. The conditions’ ability to establish rank-invariance with respect to forecast characteristics, such as bias, variance and correlation, is studied via Monte Carlo simulations. An additional moment condition identifies the functional forms of the triplet {model, estimation criterion, loss} for which the effects of measurement errors on the rankings cancel altogether. Both theoretical and empirical results show the extension of admissible loss functions achieving ranking consistency in forecast evaluations.