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Autoregressive Errors in Singular Systemsof Equations

Published online by Cambridge University Press:  11 February 2009

Phoebus J. Dhrymes
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Abstract

We consider a system of m generallinear models, where the system error vector has asingular covariance matrix owing to various “addingup” requirements and, in addition, the error vectorobeys an autoregressive scheme. The paperreformulates the problem considered earlier byBerndt and Savin [8] (BS), as well as others beforethem; the solution, thus obtained, is far simpler,being the natural extension of a restrictedleast-squares-like procedure to a system ofequations. This reformulation enables usto treat all parameterssymmetrically, and discloses a set ofconditions which is different from, and much lessstringent than, that exhibited in the frameworkprovided by BS.

Finally, various extensions are discussed to (a) thecase where the errors obey a stable autoregressionscheme of order r; (b) the casewhere the errors obey a moving average scheme oforder r; (c) the case of “dynamic”vector distributed lag models, that is, the casewhere the model is formulated as autoregressive (inthe dependent variables), and moving average (in theexplanatory variables), and the errors are specifiedto be i.i.d.

Information

Type
Research Article
Information
Econometric Theory , Volume 10 , Issue 2 , June 1994 , pp. 254 - 285
Copyright
Copyright © Cambridge University Press 1994

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