Diffusion Indexes with Sparse Loadings

The use of large-dimensional factor models in forecasting has received much attention in the literature with the consensus being that improvements on forecasts can be achieved when comparing with standard models. However, recent contributions in the literature have demonstrated that care needs to be taken when choosing which variables to include in the model. A number of different approaches to determining these variables have been put forward. These are, however, often based on ad-hoc procedures or abandon the underlying theoretical factormodel. In this paper we will take a different approach to the problem by using the LASSO as a variable selection method to choose between the possible variables and thus obtain sparse loadings from which factors or diffusion indexes can be formed. This allows us to build a more parsimonious factor model which is better suited for forecasting compared to the traditional principal components (PC) approach.We provide an asymptotic analysis of the estimator and illustrate its merits empirically in a forecasting experiment based on US macroeconomic data. Overall we find that compared to PC we obtain improvements in forecasting accuracy and thus find it to be an important alternative to PC.