  In this technical note, we deal with a spectrum approximation problem arising
in THREE-like multivariate spectral estimation approaches. The solution to the
problem minimizes a suitable divergence index with respect to an a priori
spectral density. We derive a new divergence family between multivariate
spectral densities which takes root in the prediction theory. Under mild
assumptions on the a priori spectral density, the approximation problem, based
on this new divergence family, admits a family of solutions. Moreover, an upper
bound on the complexity degree of these solutions is provided.
