An evaluation of algorithms for computing the covariance function of a multivariable ARMA process

Computation of an ARMA covariance function is a common ingredient in analysis and synthesis of various problems in stochastic control, estimation and signal processing. In this paper, we present an algorithm based on simple polynomial calculations. Compared to alternative strategies, its computational load increases slowly with the order of the process. Further, it shows good numerical robustness and applies to multivariable ARMA processes, even with complex-valued coefficients.