Inverses of Schur Parametrization Procedures for Modeling Purposes

In this paper we present an approach to the inversion of the generalized Schur parametrization problem in accordance with Problem 1 formulated in [1]. We show that even the 'time-domain' statement of the innovations and modeling transformations of a higher-order process is nonlinear, the associated generalized algebraic Schur parametrization as well and its inversion are purely linear (or 'multi-linear') procedures. This result may clarify solving the nonlinear stochastic modeling problem.