An Algebraic Estimator for Large Spectral Density Matrices

We propose a new estimator of high-dimensional spectral density matrices, called ALgebraic Spectral Estimator (ALSE), under the assumption an underlying low rank plus sparse structure, as typically assumed in dynamic factor models. The ALSE is computed by minimizing quadratic loss nuclear norm l1 constraint to control latent and residual sparsity pattern. function requires input classical smoothed periodogram two threshold parameters, choice which thoroughly discussed. prove consistency both dimension p sample size T diverge infinity, well recovery pattern with probability one. then UNshrunk (UNALSE), designed minimize Frobenius respect pre-estimator while retaining optimality ALSE. When applying UNALSE standard U.S. quarterly macroeconomic dataset, we find evidence main sources comovements: real driving economy at business cycle frequencies, nominal higher frequency dynamics. article also complemented extensive simulation exercise. Supplementary materials for this are available online.