A Test Strategy for Discriminating between Autocorrelation and Misspecification in Regression Analysis: A Critical Note
批评了Thursby（1981）提出的区分模型设定错误的检验程序，指出其无法检测纯季节性自相关，且会误判特定非白噪声扰动为AR(1)扰动，同时证明其LRS检验中的非线性约束检验是多余的。
In a recent contribution to this Review, Thursby (1981) presents a general testing procedure consisting of three distinct test procedures which would permit discrimination among three alternatives of model misspecification. With respect to the null hypothesis of no problem with the regression (NP), the alternatives are, respectively, misspecified functional form (MS), AR(1) disturbances, and non-white noise disturbances (NAR) other than AR(1). Application of the test procedure in a Monte Carlo framework indicates that the procedure can be quite powerful. Concerning the specific NAR alternative of AR(2) disturbances one of the conclusions of Thursby is that as sample size increases and/or as the size of the second order parameter increases relative to the first order parameter the likelihood of selecting the correct alternative NAR tends to increase. However, in spite of the suggestive results of the Monte Carlo study, we will show that this conclusion doesn't hold for the limiting case where Pi = 0 and P2 = 0. In general, pure seasonal autocorrelation will not be detected at all. We will show also that Thursby's test procedure will characterize particular NAR-type disturbances wrongly as AR(1) disturbances. Furthermore we will prove that the stage in Thursby's LRS test where particular non-linear restrictions on coefficients are tested is superfluous. These restrictions happen to be satisfied irrespective of the type of the generation process of the disturbances. Besides, we will argue that the way Thursby interprets a significant value of his LRS test procedure is questionable for other reasons.