Simulation of Real Discrete Time Gaussian Multivariate Stationary Processes with Given Spectral Densities

Abstract

In this article we establish a simulation procedure to generate values for a real discrete time multivariate stationary process, based on a factor of spectral density matrix. We prove the convergence of the simulator, at each time epoch, to the actual process, and provide the corresponding rate of convergence. We merely assume that the spectral density matrix is continuous and of bounded variation. By using the positive root factor, we provide an extended version for the Sun and Chaika () simulator, for real univariate stationary processes.