For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a fixed time horizon [0, N] , and let T with h 0 while keeping the time span N fixed. We impose very mild regularity conditions on an underlying continuous-time model assumed to generate the data. We consider the least-squares estimate of the break date and establish consistency and convergence rate. We provide a limit theory for shrinking magnitudes of shifts and locally increasing variances. The asymptotic distribution corresponds to the location of the extremum of a function of the quadratic variation of the regressors and of a Gaussian centered martingale process over a certain time interval. We can account for the asymmetric informational content provided by the pre- and post-break regimes and show how the location of the break and shift magnitude are key ingredients in shaping the distribution. We consider a feasible version based on plug-in estimates, which provides a very good approximation to the finite sample distribution. We use the concept of Highest Density Region to construct confidence sets. Overall, our method is reliable and delivers accurate coverage probabilities and relatively short average length of the confidence sets. Importantly, it does so irrespective of the size of the break.

翻译：为了对线性回归模型进行部分结构改变,并一次性中断,我们开发了一个连续记录零星框架,以建立断裂日期的推算方法。我们有一个连续的记录零星框架,在固定的时间范围[0,N] 里,我们有T观测,取样频率 h 在一个固定的时间范围[0] 上,让T h 0,同时保持时间间隔N 固定。我们为生成数据而假设的一个基本的连续时间模型规定了非常温和的常规性条件。我们考虑断裂日期的最小估计,并确定一致性和趋同率。我们为折叠变幅度的缩小和地方差异提供了一种限制理论。无记录分布与递减幅度和地方差异的增加值的极限相对应,无记录分布与递减递减者的二次变量变化和高斯中心马丁格尔进程在一定时间间隔内的一个函数的极限值位置。我们可以考虑断裂前和后制度提供的不对称信息内容,并表明断裂幅度和转移幅度是决定分配的关键因素。我们考虑基于插点估计的可行版本,它为有限的抽样分布的极近近近近近近的缩度分布。我们使用了最准确性的方法。我们总的信心度的断断断断断断度和稳定度。