Structural Breaks in Time Series

过去二十年来，时间序列趋势和变化的统计建模吸引了许多统计学家。这是因为当数据表明趋势或变化时，有一系列的应用，因此它也导致了许多有趣的理论问题，在这个项目中，我们希望集中精力发展一系列相关数据的统计分析技术（时间序列），即通过特定的测试或监测程序检测某些模型假设中的结构突变（变点）。由于应用程序的数据集通常不满足某些独立或相同分布的假设，我们的目标是进一步开发相关数据的变点方法。我们的想法是修改现有的程序，已经开发的独立的情况下，拥有一定的依赖结构的模型，并考虑到这些特定的依赖关系在设计的计划。进一步的目标是获得相应的理论结果的多元时间序列，再次根据应用的要求。

Statistical modelling of trends and changes in time series has attracted many statisticians in the last two decades. The reason is that there is a whole spectrum of applications when data indicate trend(s) or change(s) and as a consequence it also results in a number of interesting theoretical problems.In this project we want to focus on developing techniques for the statistical analysis in series of dependent data (time series), that is to detect structural breaks (change-points) in certain model assumptions via specific testing or monitoring procedures. Since data sets from applications typically do not satisfy certain assumptions of independence or identical distributions, we aim at further developing change-point methods for dependent data. The idea is to modify existing procedures, which have been developed for the independent case, to models possessing certain dependency structures, and taking these specific dependencies into account in the design of the schemes. A further goal is to obtain corresponding theoretical results for multivariate time series, again according to the requirements from applications.