Mathematical Sciences: Time Series Models and Extreme Value Theory

数学科学：时间序列模型和极值理论

• 批准号: 9504596
• 负责人: Richard Davis
• 金额: $ 21万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-15 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504596&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Time; Series; Models

Proposal: DMS 9504596 PI(s): Richard Davis, Murray Rosenblatt, Peter Brockwell Institution: Colorado State Title: Times Series Models and Extreme Value Theory Abstract: The research is concerned with problems of estimation and research for time series models whose theory is not yet fully understood. The standard linear Gaussian models for time series data are inadequate to describe many of the time series observed in practice so it is important to develop techniques for estimation and prediction based on more general models. Efficient estimation procedures and prediction techniques for non-causal and non-invertible ARMA processes are developed and a study made of the theory and application of continuous-time linear and non-linear ARMA processes. Extreme value theory for linear and non-linear models is also investigated. Existing methods of forecasting are based on assumptions which are frequently not satisfied by observed economic and scientific time series data. This research develops methods of analysis and forecasting for a more general class of time series models, leading to more accurate forecasting of series which do not meet the restrictive assumptions of the classical theory.

提案：DMS 9504596 PI（S）：理查德·戴维斯，默里·罗森布拉特，彼得·布罗克韦尔机构：科罗拉多州的标题：时代序列模型和极值理论摘要：研究与理论尚未完全理解的时间序列模型的估计问题和研究有关。时间序列数据的标准线性高斯模型不足以描述在实践中观察到的许多时间序列，因此根据更一般的模型开发估计和预测技术很重要。开发了非毒物和不可抗ARMA过程的有效估计程序和预测技术，并研究了连续时间线性和非线性ARMA过程的理论和应用的研究。还研究了线性和非线性模型的极值理论。 现有的预测方法是基于通常无法通过观察到的经济和科学时间序列数据来满足的假设。这项研究开发了分析方法和预测更通用的时间序列模型，从而更准确地预测了串联的预测，这些预测不符合经典理论的限制性假设。