It is shown that the algorithms for determining the generating function and prediction error matrix of multivariate stationary stochastic processes developed by Weiner and Masani (1957, 1958) and later by Masani (1960) will work in some more general setting.
"On the Weiner-Masani Algorithm for Finding the Generating Function of Multivariate Stochastic Processes." Ann. Probab. 16 (4) 1854 - 1859, October, 1988. https://doi.org/10.1214/aop/1176991602