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Extremal Behavior of Time Series: Refined Models, Analysis and Inference

时间序列的极值行为：精细模型、分析和推理

基本信息

批准号：
213730548
负责人：
Professorin Dr. Anja Janßen
金额：
--
依托单位：
Bereich Mathematische Statistik und Stochastische Prozesse
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2014-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/213730548?language=en
关键词：
Extremal Behavior Time Series Refined

项目摘要

The aim of this project is the development of new probabilistic and statistical methods which allow for a refined description of the extremal behavior of asymptotically independent time series, i.e. time series which show no clustering of extreme values in the limit. So far, a well explored theory about time series extremes exists only in the asymptotically dependent case. However, the “classical” asymptotic approach of extreme value theory neglects the fact that a variety of different behaviors may evolve in the “pre-asymptotic” behavior of a time series. For example, many asymptotically independent time series models show a decent amount of clustering of large values in finite samples sizes. By a combination of models for asymptotically independent random vectors and methods of asymptotically dependent time series, we aim at a refinement of the tools of extreme value theory that allow for a better description and distinction of different types of asymptotic independence. We tackle both the probabilistic aspects by the development of new limit processes for cases in which classic theory gives only degenerate results, and the statistical side by giving estimators for different aspects of extremal dependence and statistical procedures for model estimation and validation. A prominent example of asymptotically independent time series is the well-known class of stochastic volatility models. Therefore, a special focus is laid on the analysis of financial time series, especially with regard to the suitability of this class for modeling the extremes of financial data.

该项目的目的是开发新的概率和统计方法，以便精确描述渐近独立时间序列的极值行为，即在极限中没有极值聚集的时间序列。到目前为止，一个很好的探索理论的时间序列极值只存在于渐近相关的情况下。然而，极值理论的“经典”渐近方法忽略了一个事实，即各种不同的行为可能演变的“前渐近”行为的时间序列。例如，许多渐近独立的时间序列模型在有限的样本大小中显示出大量的大值聚类。通过渐近独立的随机向量模型和渐近相关的时间序列的方法相结合，我们的目标是改进极值理论的工具，允许更好地描述和区分不同类型的渐近独立性。我们解决的概率方面的发展，新的极限过程的情况下，经典理论只给出退化的结果，和统计方面的极值依赖和统计程序模型估计和验证的不同方面的估计。渐近独立时间序列的一个突出例子是众所周知的一类随机波动率模型。因此，一个特别的重点放在金融时间序列的分析，特别是关于这个类的建模金融数据的极端的适用性。