Autoregressive Errors in Singular Systems of Equations
研究了m个一般线性模型组成的系统，其误差向量因加总约束而协方差矩阵奇异，且服从自回归过程。本文重新表述了问题，得到比Berndt和Savin更简单的解，并讨论了多种扩展情形。
We consider a system of m 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 system of equations . This reformulation enables us to treat all parameters symmetrically , and discloses a set of conditions which is different from, and much less stringent than, that exhibited in the framework provided by BS. Finally, various 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 formulated as autoregressive (in the dependent variables), and moving average (in the explanatory variables), and the errors are specified to be i.i.d.