STRUCTURAL CHANGE IN AR(1) MODELS
研究了AR(1)模型中未知时点单一结构突变下最小二乘估计的一致性及其极限分布，特别关注单位根情形，发现无论突变点估计位置如何，单位根总能被一致估计。
This paper investigates the consistency of the least squares estimators and derives their limiting distributions in an AR(1) model with a single structural break of unknown timing. Let β 1 and β 2 be the preshift and postshift AR parameter, respectively. Three cases are considered: (i) |β 1 | < 1 and |β 2 | < 1; (ii) |β 1 | < 1 and β 2 = 1; and (iii) β 1 = 1 and |β 2 | < 1. Cases (ii) and (iii) are of particular interest but are rarely discussed in the literature. Surprising results are that, in both cases, regardless of the location of the change-point estimate, the unit root can always be consistently estimated and the residual sum of squares divided by the sample size converges to a discontinuous function of the change point. In case (iii), [circumflex over beta] 2 does not converge to β 2 whenever the change-point estimate is lower than the true change point. Further, the limiting distribution of the break-point estimator for shrinking break is asymmetric for case (ii), whereas those for cases (i) and (iii) are symmetric. The appropriate shrinking rate is found to be different in all cases.