In this paper we study the theoretical properties of the simultaneous multiscale change point estimator (SMUCE) proposed by Frick et al. (2014) in regression models with dependent error processes. Empirical studies show that in this case the change point estimate is inconsistent, but it is not known if alternatives suggested in the literature for correlated data are consistent. We propose a modification of SMUCE scaling the basic statistic by the long run variance of the error process, which is estimated by a difference-type variance estimator calculated from local means from different blocks. For this modification we prove model consistency for physical dependent error processes and illustrate the finite sample performance by means of a simulation study.

中文翻译：

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相关数据的多尺度变化点检测

在本文中，我们研究了 Frick 等人提出的同时多尺度变化点估计器（SMUCE）的理论特性。(2014) 在具有相关误差过程的回归模型中。实证研究表明，在这种情况下，变化点估计是不一致的，但不知道文献中为相关数据建议的替代方案是否一致。我们提出了对 SMUCE 的修改，通过误差过程的长期方差来缩放基本统计量，这是通过从不同块的局部均值计算的差异型方差估计器来估计的。对于这种修改，我们证明了物理相关误差过程的模型一致性，并通过模拟研究说明了有限样本的性能。