基于Sieve Bootstrap方法的长记忆过程变点研究与应用

项目名称： 基于Sieve Bootstrap方法的长记忆过程变点研究与应用

项目编号： No.11301291

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 陈占寿

作者单位： 青海师范大学

项目金额： 22万元

中文摘要： 本项目基于Sieve Bootstrap方法研究长记忆过程持久性变点、结构变点和方差变点的在线监测、后验检验及应用问题。主要内容有：（1）基于封闭式变点监测方法，提出监测含趋势项的长记忆过程平稳性、非平稳性及持久性变点的核加权方差比率方法和CUSUM比率方法。（2）基于开放式变点监测方法，提出一种对不同时刻出现的变点都有效的改进CUSUM方法，来分别监测含长记忆噪声的线性回归和非参数回归模型结构变点、方差变点及长记忆过程中的持久性变点。（3）提出一种既能避免估计尺度参数，检验势又相对更高的修正比率方法，来检验和估计长记忆过程均值变点、方差变点及持久性变点。此外，上述所有内容将在长记忆过程含有方差无穷厚尾新息的条件下继续研究，并提出既能够避免估计长记忆参数和厚尾指数，又能提高检验势的一致Sieve Bootstrap近似方法。最后通过数值模拟和实证分析说明所提新方法的有效性和可行性。

中文关键词： 长记忆时间序列；变点；Sieve bootstrap方法；在线监测；

英文摘要： This research studies on-line monitoring, retrospective test and application problems of structural change, variance change and persistence change in long memory process based on Sieve Bootstrap method. The contents are as follows: (1) Based on the close ended change point monitoring scheme, we will propose a kernel weighted variance ratio statistic and a CUSUM ratio statistic to monitor the stationarity, nonstationarity, and persistence change in long memory process with deterministic trend. (2) Based on the open ended change point monitoring scheme, we will propose an improved CUSUM method to monitor the structural change, vanriance change in linear regression and nonparametric regression models with long memory noise, and persistence change in long memory process. The improved CUSUM method is efficient for all those changes occurring at any time. (3) A modified ratio procedure will be proposed to test and estimate the mean change, variance change and changes in presistence. The modification can not only avoid estimating the scale parameter of model, but also can improve the test power. In addition, the proposed methods will be studied further in the long memory processes with infinite variance heavy-tailed innovations, and a concictent Sieve Bootstrap asymptotic method will be constructed for all above propo

英文关键词： Long memory time series；Change point；Sieve bootstrap method；Online monitoring；