Spectral estimation can be performed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be seen as a new parametric spectral estimation problem. This interpretation implies that the THREE-like solution is optimal in terms of closeness to the correlogram over a certain parametric class of spectral densities describing ARMA models, enriching in this way its meaningfulness. (C) 2015 Elsevier Ltd. All rights reserved.