Mathematical Sciences: Time Series, Extreme Values and Stochastic Models

数学科学：时间序列、极值和随机模型

• 批准号: 9006422
• 负责人: Richard Davis
• 金额: $ 1.67万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006422&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Time; Series; Extreme; Mathematical; Sciences; Time; Series; Extreme

The principal investigators will work in the area of time series analysis and stochastic modeling. The work is divided into two parts. The first part is concerned with problems of estimation and prediction for time series models whose theory is not yet fully understood. These include non-linear, heavy tailed and non-Gaussian processes, all of which play a role in the modelling of real time series data. Efficient estimation and prediction procedures for such series will be sought and their properties will be investigated. Some relatively unexplored models will be considered and some new techniques for state-space modelling of multivariate time series will be investigated. The second part deals with extreme value theory, particularly the interplay between extreme value methods, point processes, asymptotic theory and the application of these ideas to linear, bilinear and general stationary processes.

主要研究人员将在时间序列分析和随机建模领域工作。 工作分为两个部分。 第一部分涉及估计和预测时间序列模型的问题，这些模型的理论尚未完全理解。 其中包括非线性，重型尾巴和非高斯过程，所有这些过程在实时数据的建模中起着作用。 将寻求该系列的有效估计和预测程序，并将研究其性质。 将考虑一些相对未开发的模型，并将研究一些用于多元时间序列的状态空间建模的新技术。 第二部分涉及极端价值理论，尤其是极值方法，点过程，渐近理论以及这些思想在线性，双线性和一般固定过程中的相互作用。