ARMA Representation of Random Processes

Abstract

ARMA models of the same order for AR and MA components are used for the characterization and simulation of stationary Gaussian multivariate random processes with zero mean. The coefficient matrices of the ARMA models are determined so that the simulated process will have the prescribed correlation function matrix. To accomplish this, the two‐stage least squares method is used. The ARMA representation thus established permits one, in principle, to generate sample functions of infinite length and with such a speed and computational mode that even real time generations of the sample functions can be easily achieved. The numerical example indicates that the sample functions generated by the method presented herein reproduce the prescribed correlation function matrix extremely well despite the fact that these sample functions are all very long. This is seen from the closeness between the analytically prescribed auto‐ and cross‐correlation functions and the corresponding sample correlations computed from the generated sample functions.