Variable Selection in Predictive Regressions

This chapter reviews methods for selecting empirically relevant predictors from a set of N potentially relevant ones for the purpose of forecasting a scalar time series. I first discuss criterion based procedures in the conventional case when N is small relative to the sample size, T . I then turn to the large N case. Regularization and dimension reduction methods are then discussed. Irrespective of the model size, there is an unavoidable tension between prediction accuracy and consistent model determination. Simulations are used to compare selected methods from the perspective of relative risk in one period ahead forecasts.