Mathematical Sciences: Nonlinear Time Series Analysis

数学科学：非线性时间序列分析

• 批准号: 9301193
• 负责人: Rong Chen
• 金额: $ 4万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301193&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonlinear; Time; Series

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.

本课题涉及非线性时间序列分析。它有四个主要目标。第一个目标是通过非参数平滑技术开发非线性时间序列建模的新方法。本研究是PI和Tsay在过去几年对功能系数AR模型和非线性加性AR模型工作的延续。见Chen and Tsay （1993a, 1993b）。本文的研究结果将提高非线性时间序列模型的适用性。本研究的第二个目标是研究二元过程驱动的切换回归模型。对一般开关结构提出了一种统一的处理方法，并介绍了一种区分随机（独立）开关回归模型和马尔可夫链驱动模型的检验方法。第三个目标是研究寻找开环阈值AR模型指标变量的新方法。提出了几种方法来克服开环阈值AR模型使用中遇到的困难。特别地，提出了两种算法和一些图形工具来确定合适的指标变量。最后的目的是研究一些非线性时间序列模型的遍历条件。所得结果将有助于更好地理解非线性模型，并为建立用于非线性时间序列分析的各种非参数统计量的渐近性质奠定基础。