Forecasting using cross-section average-Augmented time series regressions

There is a large and growing body of literature concerned with forecasting time series variables by the use of factor-Augmented regression models. The workhorse of this literature is a two-step approach in which the factors are first estimated by applying the principal components method to a large panel of variables, and the forecast regression is then estimated, conditional on the first-step factor estimates. Another stream of research that has attracted much attention is concerned with the use of cross-section averages as common factor estimates in interactive effects panel regression models. The main justification for this second development is the simplicity and good performance of the cross-section averages when compared with estimated principal component factors. In view of this, it is quite surprising that no one has yet considered the use of cross-section averages for forecasting. Indeed, given the purpose to forecast the conditional mean, the use of the crosssectional average to estimate the factors is only natural. The present paper can be seen as a reaction to this. The purpose is to investigate the asymptotic and small-sample properties of forecasts based on cross-section average augmented regressions. In contrast to most existing studies, the investigation is carried out while allowing the number of factors to be unknown.