June 2015, with B. Kelly
We forecast a single time series using many predictor variables with a new estimator called the three-pass regression filter (3PRF). It is calculated in closed form and conveniently represented as a set of ordinary least squares regressions. 3PRF forecasts are consistent for the infeasible best forecast when both the time dimension and cross section dimension become large. This requires specifying only the number of relevant factors driving the forecast target, regardless of the total number of common factors driving the cross section of predictors. The 3PRF is a constrained least squares estimator and reduces to partial least squares as a special case. Simulation evidence confirms the 3PRF’s forecasting performance relative to alternatives. We explore two empirical applications: Forecasting macroeconomic aggregates with a large panel of economic indices, and forecasting stock market returns with price–dividend ratios of stock portfolios.