标题： 使用许多噪声的经济预测 显示英文标题

标题： Economic Forecasts Using Many Noises

摘要： 本文解决了一个经济预测中的关键问题：纯噪声是否真的缺乏预测能力？ 经济学家通常进行变量选择以从预测因子中消除噪声。 然而，我们证明了一个有力的结果，即在大多数经济预测中，将噪声包含在预测中所带来的好处大于将其排除。 此外，如果预测因子的总数不够大，有意识地添加更多噪声可以带来更优的预测性能，优于依赖降维的基准预测因子。 其直觉在于经济预测信号在回归系数中密集分布，即使大量预测因子构成纯噪声，也能保持适度的预测偏差，同时分散整体方差。 我们的一个实证演示表明，有意识地向Welch和Goyal（2008）数据集中添加300~6,000个纯噪声，在预测美国年度股权溢价时实现了显著的10%样本外R平方准确率。 该性能超过了大多数复杂的机器学习模型。 显示英文摘要

摘要： This paper addresses a key question in economic forecasting: does pure noise truly lack predictive power? Economists typically conduct variable selection to eliminate noises from predictors. Yet, we prove a compelling result that in most economic forecasts, the inclusion of noises in predictions yields greater benefits than its exclusion. Furthermore, if the total number of predictors is not sufficiently large, intentionally adding more noises yields superior forecast performance, outperforming benchmark predictors relying on dimension reduction. The intuition lies in economic predictive signals being densely distributed among regression coefficients, maintaining modest forecast bias while diversifying away overall variance, even when a significant proportion of predictors constitute pure noises. One of our empirical demonstrations shows that intentionally adding 300~6,000 pure noises to the Welch and Goyal (2008) dataset achieves a noteworthy 10% out-of-sample R square accuracy in forecasting the annual U.S. equity premium. The performance surpasses the majority of sophisticated machine learning models.