  The partial stochastic realization of periodic processes from finite
covariance data has recently been solved by Lindquist and Picci based on convex
optimization of a generalized entropy functional. The meaning and the role of
this criterion have an unclear origin. In this paper we propose a solution
based on a nonlinear generalization of the classical Yule-Walker type equations
and on a new iterative algorithm which is shown to converge to the same
(unique) solution of the variational problem. This provides a conceptual link
to the variational principles and at the same time yields a robust algorithm
which can for example be successfully applied to finite-interval smoothing
problems providing a simpler procedure if compared with the classical
Riccati-based calculations.
