Mathematical Sciences: Time Series Models and Extreme Value Theory

提案：DMS 9504596 PI（s）：Richard Davis，Murray Rosenblatt，Peter布罗克韦尔机构：科罗拉多州标题：时间序列模型和极值理论 摘要： 这项研究涉及的问题估计和 时间序列模型的研究，其理论尚未 完全理解标准线性高斯模型 时间序列数据不足以描述许多 在实践中观察到的时间序列，因此重要的是 发展估算和预测技术， 更一般的模型。有效的估计程序和 非因果和不可逆的预测技术 发展了阿尔马过程，研究了 连续时间线性和 非线性阿尔马过程。极值理论 线性和非线性模型也进行了研究。 现有的预测方法是基于假设的 这往往不能满足所观察到的经济 科学时间序列数据。这项研究开发了 分析和预测的方法，更一般 类的时间序列模型，导致更准确的 不符合限制条件的序列的预测 古典理论的假设。

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.