Data Segmentation and High Dimensional Time Series Analysis

在我的研究中，我将研究时间序列数据分割，特别是在假设检验框架下对多变量时间序列进行多变点分析。我将首先着重于开发一个低维向量自回归过程的移动和过程，并推导其统计保证。然后将其扩展到高维数据，采用结构化VAR模型进行计算可行性。我将探讨所提出的方法在经济和金融数据中的应用。有可能研究它们与现代推理问题（如顺序测试）和网络分析的联系。在项目的后期，我可能会研究其他时间序列结构，如波动性模型，或其他类型的非平稳性，如协整。作为一个总体主题，我的目标是为从业者开发一种方法论。因此，除了研究所提出的方法的统计保证外，我还将努力开发快速有效的算法，并将其实现作为R语言的软件包提供。

In my research, I will study time series data segmentation, particularly multiple change point analysis for multivariate time series in the hypothesis testing framework. I will first focus on developing a moving sum procedure for low-dimensional vector autoregression processes and deriving its statistical guarantees. This will then be extended to high-dimensional data, adopting a structured VAR model for computational feasibility. I will explore the applications of proposed methodologies to economic and financial data. There is potential to study their links to modern inference problems, such as sequential testing, and to network analysis. Later into the project, I may investigate other time series structures, such as volatility models, or other types of non-stationarity, such as cointegration. As a general theme, my aim is to develop a methodology for practitioners. Therefore, along with investigating into statistical guarantees of the proposed methodologies, I will also endeavour to develop fast and efficient algorithms and make their implementations available as software packages in the R language.