[1]张立文,周秀轻.P阶自回归模型中的变点检验问题[J].南京师范大学学报(自然科学版),2010,33(02):13-17.
 Zhang Liwen,Zhou Xiuqing.Testing for Change-Point of the P-Order Autoregressive Time Series Model[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(02):13-17.
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P阶自回归模型中的变点检验问题()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第33卷
期数:
2010年02期
页码:
13-17
栏目:
数学
出版日期:
2010-06-20

文章信息/Info

Title:
Testing for Change-Point of the P-Order Autoregressive Time Series Model
作者:
张立文;周秀轻;
南京师范大学数学科学学院, 江苏南京210097
Author(s):
Zhang LiwenZhou Xiuqing
School of Mathematical Sciences,Nanjing Normal University,Nanjing 210097,China
关键词:
变点 自回归模型 极大似然法 最小二乘法
Keywords:
chang e-po int au to regress ive models them ax imum likelihood the least squares me thod
分类号:
O212.1
摘要:
变点问题是统计学中一个较新的课题.本文讨论了p阶自回归模型中的变点检验问题,对于自回归模型在模型的白噪声序列的方差σ 2未知的条件下,分别利用最大似然估计方法和最小二乘法给出了变点的检验统计量,并得到统计量的渐近分布,最后给出了证明.
Abstract:
Change-po int prob lem is a new top ic in the statistics. In th is paper, w e consider the change-point problem in the p-o rder autoregressive tim e ser ies m ode .l When the var iance σ2 is unknown, w e use them ax inum likelihood m ethod and the least squares estim a tion to g ive the test statistics and atta in the ir asym ptotic distributions for the change-po int. W e g iv e the ir proofs at last.

参考文献/References:

[ 1]Page E S. Continuous inspec tion schem es[ J]. B iome tr ika, 1954, 41( 1 /2): 100-115.
[ 2]陈希孺. 只有一个转变点的模型的假设检验和区间估计[ J] . 中国科学A 辑, 1998, 8: 817-827.
[ 3]Cs rg  , H orv th. Lim it Theo rem s in Chang-Po ints Ana lysis[M ]. N ew York: JohnW iley& Sons, 1997.
[ 4]王黎明. 变点统计分析的研究进展[ J]. Statistical Research, 2003, 1: 50-51.
[ 5]H ink ley DV. In fe rence about the change-po int in asequence of random var iables[ J]. B iom etrika, 1970, 56( 1): 1-17.
[ 6]H aw kins D L. A sim ple least squares m ethod for estima ting a change in m ean[ J]. Comm un ications in Statistics-S imu la tion, 1986, 15( 3): 655-679.
[ 7]W orse ley K J. Confidence reg ions and test fo r a change-po int in a sequence of exponentia l fam ily random var iables[ J]. B-i om etr ika, 1986, 73( 1): 91-104.
[ 8]陈希孺. 变点统计分析简介[ J]. 数理统计分析简介, 1991, 12: 52-58.
[ 9]HuangW T, Chang Y P. Nonparam etric estim ation in chage-po int model[ J]. Journal o f S tatistica l P lann ing and In ference, 1993, 35( 3): 335-347.
[ 10]Ja ru skov D. Testing appearance of linear trend[ J]. Journa l o f Statistica l P lann ing and In fe rence, 1998, 70( 2 ): 263- 276.
[ 11]H u kov M. G radua l changes versus abrupt changes[ J] . Journal of Sta tistica l Plann ing and In ference, 1999, 76( 1 /2): 109-125.
[ 12]Gupta A K, Ram anayaske A. Change points w ith linear trend for the exponentia l d istr ibution[ J]. Journa l o f Sta tistica l Plann ing and In ference, 2001, 93( 1) : 181-195.
[ 13]P io trKokoszka, Rem ig ijus Le ipus. Change-po int estima tion in ARCH models[ J] . Bernou ll,i 2000, 6( 3): 513-539.
[ 14]Sangyeo l Lee, Jeongcheo lH a. The cusum test for param e ter change in tim e ser ies m ode ls[ J]. Scandinav ian Journa l of Statistics, 2003, 30( 4): 781-796.
[ 15]T imm er D H, P igna tie llo J J. Change po int estim ates for the param eters o f an AR ( 1) process[ J]. Qua lity and Re liability Eng ineer ing In ternationa,l 2003, 19( 4): 355-369.
[ 16]王黎明. Testing fo r change-po int o f the first-o rder auto regress ive time ser ies m ode ls[ J]. 应用概率统计, 2008, 24( 1): 28-36.
[ 17]R ichard A Dav is, Daw e iH uang, Y -i Ch ing. Testing fo r a change in the param eter values and o rder o f an autoreg ressive model [ J]. The Annals o f S tatistic, 1995, 23( 1): 282-304.
[ 18]Ku lperg erR J. On the residua ls o f au to reg ressive processes and po lunom ia l reg ression[ J]. Stochastic Processes and their Applica tions, 1985, 21( 1): 107-118.

备注/Memo

备注/Memo:
基金项目: 国家自然科学基金( 10626028) . 通讯联系人: 周秀轻, 博士, 副教授, 研究方向: 生存分析和回归分析. E-mail:zhouxiuqing@ njnu. edu. cn
更新日期/Last Update: 2013-04-08