On the Wiener-Masani algorithm for finding the generating function of multivariate stochastic processes (Q1111234)

It is shown that some algorithms for determining the generating function, the prediction error matrix and an autoregressive representation for the linear least-squares predictor of a multivariate stationary stochastic process developed by \textit{N. Wiener} and \textit{P. Masani} [Acta Math. 98, 111-150 (1957); and ibid. 99, 93-137 (1958; Zbl 0080.130)] work when the spectral density can be factored as \[ f(e^{i\theta})=P(e^{i\theta})g(e^{i\theta})P^*(e^{i\theta}), \] where \(g(e^{i\theta})\) is a new spectral density satisfying Masani's condition and \(P(e^{i\theta})\) is a polynomial of a special type.