Topics in Nonlinear and Functional Time Series

非线性和函数时间序列主题

• 批准号: 0905400
• 负责人: Lajos Horvath
• 金额: $ 25万
• 依托单位: University of Utah
• 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 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905400&HistoricalAwards=false
• 关键词: Topics; Nonlinear; Functional; Time; Series

The investigators examine statistical inference techniques for nonlinear and functional time series models that work in both stationary and nonstationary regimes, thereby providing unified procedures that help advance statistical theory. Since determining whether a given set of (functional) observations is stationary can be a vexing problem, the proposed research also helps to lighten the statistical analysis for practitioners. Moreover, the investigators develop a new framework to deal with dependent Hilbert space-valued random functions which is both mathematically challenging and important for statistical applications in various areas such as finance, econometrics, astronomy, geophysics, climatology and genetics. This research is based on delicately fusing elements of statistical and probability theory with time series and functional data analysis.The investigators' research is aimed at providing flexible statistical tools for practitioners that are less sensitive to underlying model assumptions and time dependent changes in environment. In view of the economic crisis in the Fall of 2008, this seems to be of particular importance for the analysis of financial data, but may also prove relevant in other scientific fields such as climatology. To enhance our understanding of these complex scientific questions, the investigators' research will provide novel data-analytic tools for practitioners by advancing statistical theory.

研究人员研究了在平稳和非平稳状态下工作的非线性和功能性时间序列模型的统计推断技术，从而提供了有助于推进统计理论的统一程序。由于确定一组给定的(功能)观测是否是平稳的可能是一个令人烦恼的问题，拟议的研究也有助于减轻从业者的统计分析。此外，研究人员开发了一种新的框架来处理相依的希尔伯特空间值随机函数，这在数学上既具有挑战性，又对金融、计量经济学、天文学、地球物理学、气候学和遗传学等不同领域的统计应用具有重要意义。这项研究的基础是将统计和概率理论的元素与时间序列和功能数据分析巧妙地融合在一起。研究人员的研究旨在为对潜在模型假设和环境中的时间依赖变化不那么敏感的从业者提供灵活的统计工具。鉴于2008年秋季的经济危机，这似乎对金融数据的分析特别重要，但也可能被证明与气候学等其他科学领域有关。为了加深我们对这些复杂科学问题的理解，研究人员的研究将通过推进统计理论为从业者提供新的数据分析工具。