Autoregressive Errors in Singular Systems of Equations

We consider a system of <italic>m</italic> general linear models, where the system error vector has a singular covariance matrix owing to various “adding up” requirements and, in addition, the error vector obeys an autoregressive scheme. The paper reformulates the problem considered earlier by Berndt and Savin [8] (BS), as well as others before them; the solution, thus obtained, is far simpler, being the natural extension of a restricted least-squares-like procedure to a <italic>system of equations</italic>. This reformulation enables us to treat <italic>all parameters symmetrically</italic>, and discloses a set of conditions which is different from, and much less stringent than, that exhibited in the framework provided by BS.