This article addresses the problem of forecasting a single time series using a large number of predictors, where the number of predictors (N) can be much larger than the number of time series observations (T). The authors propose using principal components to summarize the predictors, which are then estimated from the data. They show that these estimates are consistent and asymptotically efficient, meaning that the difference between the feasible forecasts and the optimal forecasts constructed using the actual values of the factors converges to zero as both N and T grow large. The article also discusses the robustness of these results to time variation in the factor model, demonstrating that the consistency holds even when there is small and idiosyncratic shifts in the factor loadings. The authors provide a Monte Carlo study to evaluate the finite-sample performance of the method and apply it to macroeconomic forecasting, showing significant improvements over conventional models.This article addresses the problem of forecasting a single time series using a large number of predictors, where the number of predictors (N) can be much larger than the number of time series observations (T). The authors propose using principal components to summarize the predictors, which are then estimated from the data. They show that these estimates are consistent and asymptotically efficient, meaning that the difference between the feasible forecasts and the optimal forecasts constructed using the actual values of the factors converges to zero as both N and T grow large. The article also discusses the robustness of these results to time variation in the factor model, demonstrating that the consistency holds even when there is small and idiosyncratic shifts in the factor loadings. The authors provide a Monte Carlo study to evaluate the finite-sample performance of the method and apply it to macroeconomic forecasting, showing significant improvements over conventional models.