A Generalization of the Durbin Significance Test and Its Application to Dynamic Specification
针对高阶自回归误差的方程估计中似然比检验渐近尺寸有偏的问题，提出一种类似杜宾检验的无偏新检验，并推广到动态设定问题，计算简单且参数选择更少任意性。
When estimating a single equation with an error generated by an autoregressive process of higher order than one using a sequence of likelihood ratio tests to determine the correct order, the asymptotic size of the tests will be biased because of multiple optima of the likelihood function. A new type is suggested similar to the Durbin test [2] which is not biased in this way. IN HIS ARTICLE on testing for serial correlation in the presence of lagged endogenous variables [2] Durbin proved a general theorem which gives a significance test shown to be generally asymptotically equivalent to a likelihood ratio test. This paper proposes a generalization which gives a test criterion that may be preferred to the existing test criteria insofar as it can be set up using a less arbitrary choice of the parameters to be re-estimated, and also has the advantage of being relatively simple to compute. It seems more appropriate than the general Durbin form of test for application to the dynamic specification problem discussed in the third section of this article.