OPTIMAL SIMILAR TESTS FOR STRUCTURAL CHANGE FOR THE LINEAR REGRESSION MODEL
针对正态线性回归模型，在有限样本下推导了一类最优相似检验，用于检测未知时间点的结构变化，并扩展了误差方差未知时的加权最优检验，模拟研究比较了检验功效。
This paper analyzes similar tests for structural change for the normal linear regression model in finite samples. Using the approach of Wald (1943, American Mathematical Society Transactions 54, 426–482), Hillier (1987, Econometric Theory 3, 1–44), Andrews and Ploberger (1994, Econometrica 62, 1382–1414), and Andrews, Lee, and Ploberger (1996, Journal of Econometrics 70, 9–36), we characterize a class of optimal similar tests for the existence of (possibly multiple) changepoints at unknown times. We extend the analysis of Andrews et al. (1996) by deriving weighted optimal similar tests for the case where the error variance is not known. We also show that when the sample size is large, the tests of Andrews et al. constructed by replacing the error variance with an estimate are equivalent to the optimal test derived in this paper. Power comparisons are provided by a small simulation study.