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

Multivariate Spectral Estimation based on the concept of Optimal Prediction