  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.
