Abstract: We study the time-reversibility of multivariate linear processes, introducing a necessary and sufficient condition related to linear transforms of the multivariate linear process. Conditions analogous to Cheng's for univariate non-Gaussian linear processes are also explored; these are in terms of the noise distribution and the model parameters. The exploration results in an easily verifiable set of necessary and sufficient conditions for a multivariate non-Gaussian linear process driven by a univariate noise, leaving the case of multivariate noise as a challenging open problem.
Key words and phrases: Moving average, multivariate linear process, time-reversibility.