Statistical Inference on Sets, Nonparametric Financial Time Series and Extreme Value theory

集合统计推断、非参数金融时间序列和极值理论

• 批准号: 227808441
• 负责人: Professor Dr. Enno Mammen
• 金额: --
• 依托单位: Department of Statistics
• 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 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/227808441?language=en
• 关键词: Statistical; Inference; Sets; Nonparametric; Financial

The project consists in two parts: statistical inference on sets and nonparametric financial time series. The first topic is confidence regions for nonparametric sets. The construction is based on nonparametric curve estimators. Mathematically, this requires the analysis of the distribution of suprema of smoothing estimators over manifolds. Sets of interest are e.g. level sets of curves, ridges, intersections of curves, and intersection bounds. Such sets arise from different fields of applications. The second topic is the construction of GARCH-like financial time series where the dynamics runs over a stochastic recurrence equation but where instead of conditional variances also other conditional nonparametric functionals enter into the model. Extreme value statistics is used to analyse the tail behaviour of the resulting time series and of other already studied GARCH-processes.

该项目由两部分组成：集合的统计推断和非参数金融时间序列。第一个主题是非参数集的置信区域。该构造基于非参数曲线估计器。从数学上讲，这需要分析流形上平滑估计器的上界分布。兴趣集例如曲线、脊线、曲线交点和交点边界的水平集。此类集合源自不同的应用领域。第二个主题是构建类似 GARCH 的金融时间序列，其中动态运行在随机递推方程上，但模型中也输入了其他条件非参数函数，而不是条件方差。极值统计用于分析结果时间序列和其他已研究的 GARCH 过程的尾部行为。