This article examines forecasting a single time series using a large number of predictors under an approximate factor model. The key idea is to use principal components to estimate the underlying factors that summarize the predictors. The authors show that these principal component estimates are consistent and that the resulting forecasts are asymptotically efficient. The model assumes that the predictors can be represented as a linear combination of a small number of latent factors plus idiosyncratic errors. The forecast is constructed by estimating the relationship between the target variable and the factors using linear regression. The authors demonstrate that the feasible forecast, which uses the estimated factors, converges to the infeasible forecast that would be obtained if the true factors were known. They also show that the results hold even when the factor model is temporally unstable, as long as the instability is small and the errors are weakly cross-sectionally correlated. The article also presents a Monte Carlo study showing that the principal components method performs well in finite samples, and an empirical example applying the method to forecast industrial production. The results suggest that the method can significantly improve forecast accuracy compared to conventional models using a small number of variables.This article examines forecasting a single time series using a large number of predictors under an approximate factor model. The key idea is to use principal components to estimate the underlying factors that summarize the predictors. The authors show that these principal component estimates are consistent and that the resulting forecasts are asymptotically efficient. The model assumes that the predictors can be represented as a linear combination of a small number of latent factors plus idiosyncratic errors. The forecast is constructed by estimating the relationship between the target variable and the factors using linear regression. The authors demonstrate that the feasible forecast, which uses the estimated factors, converges to the infeasible forecast that would be obtained if the true factors were known. They also show that the results hold even when the factor model is temporally unstable, as long as the instability is small and the errors are weakly cross-sectionally correlated. The article also presents a Monte Carlo study showing that the principal components method performs well in finite samples, and an empirical example applying the method to forecast industrial production. The results suggest that the method can significantly improve forecast accuracy compared to conventional models using a small number of variables.