ARCH模型分布变点监测与应用  

Online Monitoring and Application for Distributional Changes in ARCH Models

作　　者：李拂晓[1] 田铮[1,2] 陈占寿[3] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072 [2]中国科学院遥感应用研究所,北京100101 [3]青海师范大学数学系,青海西宁810000

出　　处：《数学的实践与认识》2015年第2期211-218,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11301291)

摘　　要：分布变点监测是时间序列交点分析的一个重要内容.为将分布交点监测从线性时间序列模型拓展到非线性时间序列模型,提出一种经验特征函数型的统计量监测ARCH模型误差项平方的分布变点,给出了监测统计量在原假设下的极限分布,并证明了此方法的一致性,用Bootstrap重抽样方法获得了极限分布的临界值,并和Kolmogorov-smirnov型监测统计量进行了比较.模拟结果和实例分析说明了当已观测样本量较大时,采用经验特征函数型统计量监测效果较好.Online monitoring of distributional changes is an important part of change analy- sis in time series. To extend distributional changes monitoring from linear time series models to nonlinear time series models. We propose an empirical characteristic function type statis- tic to monitor distributional changes of squared residuMs in ARCH models. The asymptotic properties of the monitoring statistic are derived under both the null of no change in dis- tribution and the alternative of a change in distribution, the critical values are obtained by bootstrap resampling method. Simulation and an example show that when the history sample is large, the empirical characteristic function type statistic is recommended compared to the Kolmogorov-smirnovtype statistic.

关 键 词：ARCH模型 分布变点检测 经验特征函数 

分 类 号：O211.61[理学—概率论与数理统计]