Analysis of Functional Time Series

函数时间序列分析

• 批准号: 0905763
• 负责人: Rong Chen
• 金额: $ 14.99万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905763&HistoricalAwards=false
• 关键词: Analysis; Functional; Time; Series

In this project the investigator develops new models, methods and associated theory under a general framework of `Functional Time Series Analysis'. Analyzing time series in a functional framework is increasingly practical and is gaining importance rapidly as more and more applications involving such data sets. There are four research projects, in the board directions of functional time series driven by dynamic processes, distributional time series driven by dynamic processes, functional ARMA models, and functional regression models with functional time series errors. They are closely related but with different focuses. The combination of the projects builds a comprehensive framework for functional time series analysis. For each project, statistical properties of the underlying models, statistical inference and predictions under these models, and the theoretical properties of the inference and prediction methods are studied. Several special and important applications are studied.Functional time series analysis can be viewed as a marriage between the traditional time series analysis and the field of functional data analysis of independent functional observations. Time series analysis is mainly interested in the dependent structure of the observations over time, the understanding the dynamic nature of the underlying process and accurate predictions of the future. Modern data collection capability has lead to broader definition of `data' and more and more observations are in the form of functions, images, and distributions. The intersection between time series analysis and functional data analysis has not been systematically explored. In this project, the investigator develops a general framework of functional time series analysis that is amenable to statistical thinking and the analysis of real problems. This project paves the way for developing a completely new research area in statistics. It has broad impact in advancing our capabilities of statistical data analysis. It aims to produce advanced statistical tools for analyzing functional time series that are encountered in many important application fields including economics and finance, environmental studies, medical and neuroscience, ecology and meteorology. The project also actively engages in activities related to education and research training of graduate and undergraduate students, especially attracting minority and women students into the field of statistics and statistical applications.

在这个项目中，研究者在“函数时间序列分析”的一般框架下发展了新的模型、方法和相关理论。在函数框架中分析时间序列变得越来越实用，并且随着越来越多的应用涉及此类数据集而迅速变得重要起来。在动态过程驱动的函数时间序列的板方向、动态过程驱动的分布时间序列、函数ARMA模型和具有函数时间序列误差的函数回归模型方面有四个研究项目。它们密切相关，但侧重点不同。这些项目的结合为功能性时间序列分析建立了一个全面的框架。对于每个项目，研究了基础模型的统计特性，这些模型下的统计推断和预测，以及推理和预测方法的理论特性。泛函时间序列分析可以看作是传统时间序列分析与独立函数观测的泛函数据分析领域的联姻。时间序列分析主要关注观测数据随时间变化的相依结构，了解潜在过程的动态性质，以及对未来的准确预测。现代数据收集能力使“数据”有了更广泛的定义，越来越多的观测以函数、图像和分布的形式出现。时间序列分析和函数数据分析之间的交集还没有得到系统的探索。在这个项目中，研究人员开发了一个泛函时间序列分析的一般框架，它服从于统计思维和对实际问题的分析。这个项目为发展一个全新的统计学研究领域铺平了道路。它对提高我们的统计数据分析能力具有广泛的影响。它的目标是生产先进的统计工具，用于分析在许多重要应用领域遇到的功能性时间序列，包括经济和金融、环境研究、医学和神经科学、生态学和气象学。该项目还积极参与与研究生和本科生的教育和研究培训有关的活动，特别是吸引少数群体和女学生进入统计和统计应用领域。