AUTOREGRESSIVE ERRORS IN SINGULAR SYSTEMS OF EQUATIONS

We consider a system of m general linear models, where the system erro r vector has a singular covariance matrix owing to various ''adding up '' requirements and, in addition, the error vector obeys an autoregres sive 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 rest ricted least-squares-like procedure to a system of equations. This ref ormulation enables us to treat all parameters symmetrically, and discl oses a set of conditions which is different from, and much less string ent than, that exhibited in the framework provided by BS. Finally, var ious extensions are discussed to (a) the case where the errors obey a stable autoregression scheme of order r; (b) the case where the errors obey a moving average scheme of order r; (c) the case of ''dynamic'' vector distributed lag models, that is, the case where the model is fo rmulated as autoregressive (in the dependent variables), and moving av erage (in the explanatory variables), and the errors are specified to be i.i.d.