Conference Agenda

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, out- performing benchmark predictors relying on dimension reduction. The intuition lies in economic predictive signals being densely distributed among regression coef- ficients, 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 R2 accuracy in forecasting the annual U.S. equity premium. The performance sur- passes the majority of sophisticated machine learning models.