A spectral EM algorithm for dynamic factor models

We make two complementary contributions to e¢ ciently estimate dynamic factor mod- els: a frequency domain EM algorithm and a swift iterated indirect inference procedure for ARMA models with no asymptotic efficiency loss for any …nite number of iterations. Although our procedures can estimate such models with many series without good initial values, near the optimum we recommend switching to a gradient method that analytically computes spectral scores using the EM principle. We successfully employ our methods to construct an index that captures the common movements of US sectoral employment growth rates, which we compare to the indices obtained by semiparametric methods.