长记忆时间序列趋势项变点的CUSUM检验  

A CUSUM test for change point in trend in long memory time series

作　　者：吉毛加 陈占寿 栗慧妮 JI Mao-jia;CHEN Zhan-shou;LI Hui-ni(School of Mathematics and Statistics,Qinghai Normal University,Xining 810008,China)

机构地区：[1]青海师范大学数学与统计学院,青海西宁810008

出　　处：《青海师范大学学报（自然科学版）》2019年第1期14-20,共7页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11661067);青海省自然科学基金(2019-ZJ-920)

摘　　要：本文研究长记忆时间序列趋势项的变点检验问题.基于最小二乘拟合残差构造了一种新的CUSUM型检验统计量,在无变点原假设下证明了检验统计量的极限分布是I型分数布朗运动的泛函,在备择假设下证明了检验统计量的一致性,并提出用Sieve Bootstrap方法确定检验统计量的临界值来避免精确估计冗余参数.数值模拟结果表明,提出的新方法在原假设下能较好地控制检验水平,在备择假设下能达到满意的检验势.This paper concentrates on the problem of change point test for trend term in long memory time series.We propose a new CUSUM test which is based on the fitting residuals of least square.The derived no change point null distribution of test statistic is function of type I fractional Brownian motion,and its consistency under the alternative hypothesis are proved.Furthermore,we use sieve bootstrap method determining the critical values of the test statistic to avoid estimating redundant parameters precisely.Simulations show that the proposed method can control the empirical size well under the null hypothesis and gives satisfy empirical power under the alternative hypothesis.

关 键 词：长记忆时间序列 趋势项变点 CUSUM检验 SIEVE BOOTSTRAP 

分 类 号：TN711.6[电子电信—电路与系统]