AR systems and AR processes: the singular case

We deal with singular multivariate AR systems and the corresponding AR processes. An AR system is called singular if the variance of the white noise innovation is singular. AR processes are the stationary solutions of AR systems. In the singular case AR processes consist of a linearly regular and a linearly singular component. The corresponding Yule-Walker equations and in particular the possible non-uniqueness of their solutions are discussed. A particular canonical form is presented. Singular AR systems naturally arise as models for latent variables in dynamic factor analysis.