This paper considers forecasting a single time series using more predictors than there are time series observations. The approach is to construct a relatively few indexes, akin to diffusion indexes, which are weighted averages of the predictors, using an approximate dynamic factor model. Estimation is discussed for balanced and unbalanced panels. The estimated dynamic factors are (uniformly) consistent, even in the presence of time varying parameters and/or data contamination, and forecasts based on the estimated factors are efficient. In an application to forecasting U.S. inflation and industrial production using 224 monthly time series, these forecasts outperform various state-of-the-art benchmark models.