This paper considers methods for forecasting macroeconomic time series in a framework where the number of predictors, N, is too large to apply traditional regression models but not su¢ciently large to resort to statistical inference based on double asymptotics. Our interest is motivated by a body of empirical research suggesting that popular data-rich prediction methods perform best when N ranges from 20 to 50. In order to accomplish our goal, we examine the conditions under which partial least squares and principal component regression provide consistent estimates of a stable autoregressive distributed lag model as only the number of observations, T, diverges. We show both by simulations and empirical applications that the proposed methods compare well to models that are widely used in macroeconomic forecasting.