Structural Breaks in Time Series

在过去的二十年里，对时间序列中的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(S)或变化(S)时，有一系列的应用，因此也产生了许多有趣的理论问题。在这个项目中，我们想要开发一种统计分析技术，用于对相依数据(时间序列)的序列进行统计分析，即通过特定的测试或监控程序来发现某些模型假设中的结构性突变(变化点)。由于来自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用于相关数据的变点方法。其思想是将为独立情况开发的现有程序修改为具有某些依赖结构的模型，并在设计方案时考虑这些特定的依赖关系。进一步的目标是根据实际应用的需要，得到相应的多变量时间序列的理论结果。

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.