Monitoring Structural Changes in Dynamic Time Series Models

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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.