Monitoring Structural Changes in Dynamic Time Series Models

结构稳定性是现代时间序列分析的主要目标之一，是计量经济学、地学、工程学、气候学、计算机科学和信号处理等领域的研究热点。显然，在错误的稳定假设下，基于不稳定关系所得出的估计的统计分析是没有意义的，无疑将产生深远的后果。众所周知，用于检测特定类型的结构变化(例如，水平移动)的各种测试统计数据也对其他现象(例如，长记忆)敏感。文献中有大量的例子。这表明需要开发新的、更复杂的程序，不仅要检测现有的变化，而且还要确定管理观察到的数据的具体基本机制。出于这一需要，调查员的研究旨在开发新的最新统计方法，使人们能够更深入地了解正在审议的现象。该框架足够通用，可以包括对各种应用程序的影响。它有两个主要目标，计量经济学和气候学。(1)经济计量经济学的主要问题之一是验证或拒绝随机游走假说。通常，在上下文中使用的测试统计具有低功耗，并且通常不仅对非平稳性敏感，而且对水平移位和长记忆也敏感。提出了能够区分这些现象的新方法。(2)在气候学中，如何解释飓风、降水和气温(全球变暖、温室效应)等与天气有关的数据存在很大争议。研究人员提出了新的方法，包括检测多个中断，这将有助于获得进一步的洞察力。这位研究人员的研究关注的是检测环境中依赖时间的变化。他相信，通过开发新的和非标准的统计方法，能够为广泛的科学讨论做出贡献，这些方法将对气候学和计量经济学产生广泛影响，并将对联邦政府产生战略利益。许多问题引发了这样的问题：先前假设的模型是否仍然有效和准确，或者结构是否发生了变化，因此，模型假设必须适应新的情况。回答这个问题当然伴随着对特定结构变化的性质以及用于描述这些变化的相互竞争的模型的演变的更详细和多样化的理解的要求。

Structural stability is one of the principal objects in modern time series analysis and is of interest in fields as diverse as econometrics, geoscience, engineering, climatology, computer science and signal processing. Clearly, statistical analyses based on estimates derived from unstable relationships under the false assumption of stability are meaningless and will doubtlessly have far-reaching consequences. It is well-known that a variety of test statistics used to detect structural changes of a certain type (ie, level shifts) are also sensitive to other phenomena (ie, long memory). Examples are abundant in the literature. This indicates the need to develop new and more sophisticated procedures that not only detect existing changes but that can also identify the specific underlying mechanism that governs the observed data. Motivated by this need, the investigator's research is aimed at developing new up-to-date statistical methods that allow for a deeper understanding of the phenomenon under consideration. The framework is general enough to include ramifications to a wide variety of applications. There are two main objectives, econometrics and climatology. (1) One of the major concerns in econometrics is to validate or reject the random walk hypothesis. Commonly, test statistics used in the context have low power and are often sensitive not only to non-stationarity but also to level shifts and long memory. New methods are proposed that are able to distinguish between these phenomena. (2) In climatology, there is a great controversy how to interpret weather related data such as hurricanes, precipitation and temperatures (global warming, greenhouse effect). The investigator proposes new methods involving the detection of multiple breaks that will help to gain further insight. The investigator's research is concerned with detecting time dependent changes in environment. He believes to be able to contribute to the broad scientific discussion by developing new and nonstandard statistical methods which will have broad impacts in climatology and econometrics, and which will be of strategic interest for the federal government. Many problems invite the question if a previously assumed model is still valid and accurate or if a structural change took place, and model assumptions, hence, have to be adapted towards a new situation. Answering this questions certainly goes along with a demand for a more detailed and diversified understanding of the nature of the particular structural changes and the evolution of the competing models used to describe them.