Structural Breaks in Time Series

在过去二十年中，时间序列趋势和变化的统计建模吸引了许多统计学家。原因是，当数据显示趋势或变化时，会有一系列的应用，因此也会产生许多有趣的理论问题。在这个项目中，我们希望专注于开发在一系列相关数据（时间序列）中进行统计分析的技术，即通过特定的测试或监控程序检测某些模型假设中的结构中断（更改点）。由于来自应用程序的数据集通常不满足某些独立性或相同分布的假设，因此我们的目标是进一步开发依赖数据的变更点方法。其思想是修改为独立案例开发的现有过程，使其具有某些依赖结构的模型，并在方案设计中考虑这些特定的依赖关系。进一步的目标是根据应用的要求，对多元时间序列得到相应的理论结果。

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.