A method is described for synthesizing multichannel autoregressive (AR) random processes. The procedure allows for variable temporal and cross-channel correlation properties subject to specific constraints for correlation functions. The resulting synthesized processes provide a 'fit' in a minimum mean squared error (MMSE) sense to the correlation functions which are specified in terms of temporal and cross-channel correlation parameters of the processes. Computer simulation results are presented showing the case of a two channel AR process with various temporal and cross-channel correlations. A method is also suggested to generalize the synthesized outputs to obtain complex processes with jointly Gaussian quadrature components where the usual assumptions associated with a complex Gaussian process are relaxed.