Title: Cross-section average-based confidence intervals for diffusion index forecasts
Authors: Hande Karabiyik - VU University Amsterdam (Netherlands) [presenting]
Jean-Pierre Urbain - Maastricht University SBE (Netherlands)
Stephan Smeekes - Maastricht University (Netherlands)
Joakim Westerlund - Lund University (Sweden)
Abstract: A situation is considered where is a single time series that can be forecasted by using a set of observed regressors and a set of latent factors. We assume there exists a set of panel data variables with a large number of cross-section ($N$) and time series observations ($T$) that are affected by the same latent factors. We propose to estimate the factors by using the cross-sectional averages of the panel data variables and then use these estimates in the forecasting equation to obtain the forecasts by using the least squares estimation method. We show that when the number of panel data variables ($m$) is equal to the number of unobserved factors ($r$), predicted conditional mean of the variable to be forecasted is consistent and asymptotically normal as $\sqrt(T)/N$ goes to zero. We provide an estimation method for the variance as well that lead to a successful way of constructing confidence intervals. Additionally we show how this result fails to hold when ($m$) is not equal to ($r$).