This paper introduces an approach to reference class selection in distributional forecasting with an application to corporate sales growth rates using several co-variates as reference variables, that are implicit predictors. The method can be used to detect expert or model-based forecasts exposed to (behavioral) bias or to forecast distributions with reference classes. These are sets of similar entities, here firms, and rank based algorithms for their selection are proposed, including an optional preprocessing data dimension reduction via principal components analysis. Forecasts are optimal if they match the underlying distribution as closely as possible. Probability integral transform values rank the forecast capability of different reference variable sets and algorithms in a backtest on a data set of 21,808 US firms over the time period 1950 - 2019. In particular, algorithms on dimension reduced variables perform well using contemporaneous balance sheet and financial market parameters along with past sales growth rates and past operating margins changes. Comparisions of actual analysts' estimates to distributional forecasts and of historic distributional forecasts to realized sales growth illustrate the practical use of the method.

翻译：本文提出一种分布式预测中参考类选择的方法，并将其应用于企业销售增长率的预测，使用多个协变量作为隐含预测因子的参考变量。该方法可用于检测受（行为）偏差影响的专家预测或基于模型的预测，或通过参考类进行分布预测。参考类是一组相似实体（此处为企业），本文提出基于排序的参考类选择算法，并可选地通过主成分分析进行预处理数据降维。若预测结果与真实分布尽可能匹配，则预测为最优。概率积分变换值用于在1950年至2019年期间包含21,808家美国企业的数据集上，对不同参考变量集和算法进行回测，以评估其预测能力。特别是，基于降维变量的算法在同时使用当期资产负债表和金融市场参数、以及过往销售增长率与营业利润率变化时表现良好。实际分析师预测与分布式预测的对比，以及历史分布式预测与实现销售增长率的对比，展示了该方法的应用价值。