Mathematical Sciences: Extreme Values and Inference in Time Series Models

首席研究人员将使用他与雷斯尼克博士共同开发的渐近技术，找出与各种时间序列相关的点过程序列的极限。当点过程由归一化极值过程生成时，一般解很难得到，甚至可能不可能得到。戴维斯博士将获得这些过程的某个子类的结果。关于样本相关函数收敛的结果直接导致对自回归过程阶数的估计。该项目的第二个领域是对时间序列模型的推断。高阶自回归过程的预测问题计算复杂。利用单变量卡尔曼滤波结果进行递归预测。将与标准的最小二乘预报器进行广泛的数值比较。这些估计的收敛速度也将被调查。

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.