In this paper the authors use results to compute finite state-space or auto-regressive moving average (ARMA) models for finite-dimensional stationary discrete time processes whose covariance is given. The reason for computing such models is that the predictor formulas become finitely recursive.
Gevers, M., & Wouters, W. R. E. (1978). An innovations approach to the discrete-time stochastic realization problem. Journal “A, 19(2), 90-110. https://hdl.handle.net/2078.5/54993 (Original work published 1978)