Frequency-Band Estimation of the Number of Factors

We introduce consistent estimators for the number of shocks driving large-dimensional dynamic factor models. Our estimator can be applied to single frequencies and specific frequency bands, making it suitable for disentangling shocks affecting dynamic models with a factor model representation. Noticeably, our estimator requires the time-series and cross-section size to diverge simultaneously without any constraint, and it is free of nuisance parameters, such as penalization terms. Our methodology appears ideal for macroeconomic analysis, as one can investigate how many shocks drive the business cycle or the long run, although the applicability of our methods is much wider, given the popularity of GDFMs in economics and finance. Its small-sample performance in simulations is excellent. We apply our estimator to the FRED-QD dataset, finding that the U.S. macroeconomy is driven by two shocks: an inflationary demand shock and a deflationary supply shock. Our methodology permits one to accurately estimate the number of shocks that drive medium-sized DSGE models despite their moderate cross-sectional size.