Simulation of Stationary Random Processes: Two‐Stage MA to ARMA Approach

Abstract

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.