Best stable and invertible approximations for ARMA systems

A method is proposed for finding the best stable and invertible approximations for an autoregressive moving average (ARMA) system, relative to a general quadratic metric in the coefficient space. Mathematically, the problem is equivalent to projecting the regression and moving average vectors of the system onto the set S of coefficients of monic Schur polynomials. The geometry of S is too complex to allow the problem to be approached directly in the ARMA coefficient space. A solution is obtained by constrained steepest descent in the hypercube of reflection coefficients, which is homomorphic to S