Robust Inference for Diffusion-Index Forecasts With Cross-Sectionally Dependent Data

In this article, we propose the time-series average of spatial HAC estimators for the variance of the estimated common factors under the approximate factor structure. Based on this, we provide the confidence interval for the conditional mean of the diffusion-index forecasting model with cross-sectional heteroscedasticity and dependence of the idiosyncratic errors. We establish the asymptotics under very mild conditions, and no prior information about the dependence structure is needed to implement our procedure. We employ a bootstrap to select the bandwidth parameter. Simulation studies show that our procedure performs well in finite samples. We apply the proposed confidence interval to the problem of forecasting the unemployment rate using data by Ludvigson and Ng.