Mathematical Sciences: Extreme Values and Inference in Time Series Models

数学科学：时间序列模型中的极值和推理

• 批准号: 8802559
• 负责人: Richard Davis
• 金额: $ 7.66万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802559&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Extreme; Values; Inference

The principal investigator will use the asymptotic techniques that he developed along with Dr. Resnick, to find limits of sequences of point processes related to various time series. When the point processes are generated from normalized extreme value processes, general solutions are hard or possibly impossible to obtain. Dr. Davis will obtain results for a certain subclass of these processes. Results on convergence of the sample correlation functions lead directly to the estimation of the order of the autoregressive processes. The second area for the project is inference on the time series models. The prediction problems for high order autoregressive processes are computationally complex. Recursive prediction will be worked out using the univariate Kalman filtering results. Extensive numerical comparisons will be made with the standard least squares predictors. Rates of convergence of these estimates will be investigated as well.

主要研究者将使用他与Resnick博士一起开发的渐近技术，以找到与各种时间序列相关的点过程序列的限制。 当点过程是从归一化的极值过程产生的，一般解决方案就很难或可能无法获得。 戴维斯博士将获得这些过程的某个子类的结果。 样品相关函数收敛的结果直接导致自回旋过程的顺序估计。 该项目的第二个领域是推断时间序列模型。 高阶自回旋过程的预测问题在计算上是复杂的。 递归预测将使用单变量的卡尔曼过滤结果来制定。 将与标准最小二乘预测指标进行广泛的数值比较。 这些估计的收敛速率也将进行研究。