Statistical Inference for Long Memory and Nonlinear Time Series

长记忆和非线性时间序列的统计推断

基本信息

批准号：
0804937
负责人：
Xiaofeng Shao
金额：
$ 7.5万
依托单位：
University of Illinois at Urbana-Champaign
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2008
资助国家：
美国
起止时间：
2008-06-01 至 2011-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0804937&HistoricalAwards=false
关键词：
Statistical Inference Long Memory Nonlinear

项目摘要

The proposal aims to develop methodological and theoretical tools for statistical inference of long memory and/or nonlinear time series, for which the traditional methods and theory developed for linear ARMA-type series are not known to be applicable. Since the applications of long memory and nonlinear models are rapidly growing, there is an urgent and crucial need to either provide a theoretical justification for existing methods or propose novel methods that are able to accommodate long memory and nonlinear features. To meet this need, the investigator proposes to study the following research problems: confidence interval for spectral means and ratio statistics; Whittle estimation and diagnostic checking for fractionally integrated time series with uncorrelated but dependent errors; new tests of independence and non-correlations between two stationary time series; frequency domain semiparametric inference for bivariate fractionally integrated nonlinear time series. All of them are linked to the second order properties of the long/short time series with nonlinear features, and together, they cover a wide spectrum of important inference issues for such series.Time series with long memory and nonlinearities occur in various fields, including atmosphere science, environmental science, geophysics, hydrology, economics, finance and others. This work will greatly enhance the available methodologies and theories, provide more tools and have potential applications in all such fields. The proposed research has significant impact on education through involvement of Ph.D students directly in the proposed research and incorporation of results into graduate statistical courses.

该提案旨在开发方法和理论工具，用于长期记忆和/或非线性时间序列的统计推断，为此，为线性ARMA型型系列开发的传统方法和理论不适用。由于长期内存和非线性模型的应用正在迅速增长，因此紧急且至关重要的是，要么为现有方法提供理论上的理由，要么提出能够适应长期内存和非线性特征的新型方法。为了满足这种需求，研究人员建议研究以下研究问题：光谱平均值和比率统计数据的置信区间；对分数集成的时间序列的Whittle估计和诊断检查，这些时间序列不相关但依赖性错误；两个固定时间序列之间的独立性和非相关性的新测试；频域的半参数推断，用于分分分分集成的非线性时间序列。所有这些都与具有非线性特征的长/短期序列的二阶特性相关联，并且它们涵盖了此类系列的各种重要推理问题。具有长期记忆和非线性的时间系列在各个领域都发生，包括大气科学，环境科学，地球物理学，水文，水文，经济学，金融和其他。这项工作将大大增强可用的方法和理论，提供更多的工具并在所有此类领域中具有潜在的应用程序。拟议的研究通过直接参与Ph.D学生参与拟议的研究并将结果纳入研究生统计课程，从而对教育产生了重大影响。