A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models
通过模拟比较多种构建结构断点日期置信区间的方法，发现Elliott和Müller的方法覆盖概率最接近名义水平，但置信区间长度过大，尤其在误差序列相关或含滞后因变量时，而其他方法无此缺陷。
This article considers constructing confidence intervals for the date of a structural break in linear regression models. Using extensive simulations, we compare the performance of various procedures in terms of exact coverage rates and lengths of the confidence intervals. These include the procedures of Bai (1997 Bai, J. (1997). Estimation of a change point in multiple regressions. Review of Economics and Statistics 79:551–563.[Crossref], [Web of Science ®] , [Google Scholar]) based on the asymptotic distribution under a shrinking shift framework, Elliott and Müller (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.[Crossref], [Web of Science ®] , [Google Scholar]) based on inverting a test locally invariant to the magnitude of break, Eo and Morley (2015 Eo, Y., Morley, J. (2015). Likelihood-ratio-based confidence sets for the timing of structural breaks. Quantitative Economics 6:463–497.[Crossref], [Web of Science ®] , [Google Scholar]) based on inverting a likelihood ratio test, and various bootstrap procedures. On the basis of achieving an exact coverage rate that is closest to the nominal level, Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.[Crossref], [Web of Science ®] , [Google Scholar]) approach is by far the best one. However, this comes with a very high cost in terms of the length of the confidence intervals. When the errors are serially correlated and dealing with a change in intercept or a change in the coefficient of a stationary regressor with a high signal-to-noise ratio, the length of the confidence interval increases and approaches the whole sample as the magnitude of the change increases. The same problem occurs in models with a lagged dependent variable, a common case in practice. This drawback is not present for the other methods, which have similar properties. Theoretical results are provided to explain the drawbacks of Elliott and Müller's (2007 Elliott, G., Müller, U. (2007). Confidence sets for the date of a single break in linear time series regressions. Journal of Econometrics 141:1196–1218.[Crossref], [Web of Science ®] , [Google Scholar]) method.