Simulation of stationary random processes: Two-stage MA to ARMA approach

The determination of moving average (MA) and autoregressive moving average (ARMA) algorithms for simulating realizations of multivariate random processes with a specified, or target, spectral matrix is presented. The MA algorithm is obtained first by relying on the maximization of an energy-like quantity. Next, a technique is formulated to derive an ARMA simulation algorithm from a prior MA approximation by relying on the minimization of frequency domain errors. Finally, these procedures are critically assessed as alternatives to existing autoregressive (AR) to ARMA two-stage simulation algorithms. Examples of applications are presented.