Mathematical Sciences: Nonlinear Time Series Analysis

这个项目关注的是非线性时间序列 分析. 它有四个主要目标。 第一个目标是 开发新的非线性时间序列建模方法， 非参数平滑技术 这项研究是一个 继续开展关于函数系数AR模型的工作， 非线性加性AR模型的PI和Tsay在过去的 几年 参见Chen和Tsay（1993 a，1993 b）。结果 根据这项研究获得的将增加适用性， 非线性时间序列模型 拟议研究的第二个目标是 研究二进制进程驱动的切换回归模型。 对一般的切换提出了统一的处理方法 结构和测试程序介绍， 随机（独立）切换回归模型的判别 马尔可夫链驱动模型。 第三个目标是 研究新的方法来寻找指标变量， 开环门限AR模型 提出了几种方法 为了克服在使用开环时遇到的困难， 门限AR模型 特别是，两个算法和一些 建议使用图形工具来确定适当的指标， 变量 最后的目的是研究遍历性 一些非线性时间序列模型的条件 结果 获得将提供一个更好的理解的非线性 模型以及一个基础上，渐近性质的 非线性时间序列的各种非参数统计 可以进行分析。

This project is concerned with nonlinear time series analysis. It has four main objectives. The first objective is to develop new methods for modeling nonlinear time series via nonparametric smoothing techniques. This research is a continuation of the work on functional coefficient AR models and nonlinear additive AR models by the PI and Tsay over the last several years. See Chen and Tsay (1993a, 1993b). The results obtained under this research will increase the applicability of nonlinear time series models. The second objective of the proposed research is to investigate binary-process driven switching regression models. A unified treatment is proposed for the general switching structures and a testing procedure is introduced for discriminating a random (independent) switching regression model from a Markov-chain driven model. The third objective is to study new approaches in finding the indicator variable for an open-loop threshold AR model. Several approaches are suggested to overcome the difficulties encountered in using the open-loop threshold AR models. In particular, two algorithms and some graphical tools are proposed to identify an appropriate indicator variable. The final objective is to investigate the ergodicity conditions of some nonlinear time series models. The results obtained will provide a better understanding of the nonlinear models as well as a foundation on which asymptotic properties of various nonparametric statistics for nonlinear time series analysis can be established.