  This paper deals with the dynamic factor analysis problem for an ARMA
process. To robustly estimate the number of factors, we construct a confidence
region centered in a finite sample estimate of the underlying model which
contains the true model with a prescribed probability. In this confidence
region, the problem, formulated as a rank minimization of a suitable spectral
density, is efficiently approximated via a trace norm convex relaxation. The
latter is addressed by resorting to the Lagrange duality theory, which allows
to prove the existence of solutions. Finally, a numerical algorithm to solve
the dual problem is presented. The effectiveness of the proposed estimator is
assessed through simulation studies both with synthetic and real data.
