带有变点的方差可能无穷大的ar模型的统计推断

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1、带有变点的方差可能无穷大的AR(1)模型的统计推断庞天晓1，张丹娜21浙江大学数学系，杭州310027，中国2芝加哥大学统计系，伊利诺伊60637,美国摘要：综文的研究对象为带有结构变点的AR(1)模型,其中AR参数β在未知时刻k0发生变化,即在模型中有两个AR参数.假设这两个参数的绝对值都小于1,模型的随机干扰项为来自正态吸引场的独立同分布随机变量,数学期望为0,方差可能不存在.那么我们在本文中讨论了两个AR参数的最小二乘估计,推广了Chong的部分结论.关键词：AR(1)模型,变点,正态吸引场,最小二乘估计,极限分布.中图分类

2、号：0212.1AsymptoticinferencesforanAR(1)modelwithachangepointandpossiblyinfinitevariancePANGTian-Xiao1,ZHANGDan-Na21DepartmentofMathematics,YuquanCampus,ZhejiangUniversity,Hangzhou310027,P.R.China2DepartmentofStatistics,UniversityofChicago,5734S.UniversityAve.,Chicago,Il

3、linois60637,USAAbstract:ThebasicmodelinthispaperisanAR(1)modelwithastructuralbreakintheARparameterβatanunknowntimek0.Thatis,therearetwoARparametersinthemodel.Supposethesetwoparametersarebothsmallerthanoneinabsolutevalue,andtheinnovationsofthemodelbeasequenceofi.i.d.rand

4、omvariableswhichareinthedomainofattractionofthenormallawwithzeromeanandpossiblyinfinitevariance,thenthelimitingdistributionsfortheleastsquaresestimatorsoftheARparametersarestudiedinthepresentpaper,whichextendsomeresultsinChong.Keywords:AR(1)model,Changepoint,Domainofattr

5、actionofthenormallaw,Leastsquaresestimator,Limitingdistribution.基金项目：SupportedbytheNationalNaturalScienceFoundationofChina(No.11001236)andResearchFundfortheDoctoralProgramofHigherEducationofChina(No.J20091604).作者简介：TianxiaoPang(1979-),AssociateProfessor,E-mailaddress:tx

6、pang@zju.edu.cn;DannaZhang(1990-),PhDCandidate,E-mailaddress:zhangdanna0507@163.com.0IntroductionTherearemanystudiesintheliteratureofstructuralchangeinthepastseveraldecades,andthereaderisreferredtoMankiwandMiron[1],Mankiw,MironandWeil[2],Hansen[3]andChong[4]etal.fordeta

7、ils.ItisworthmentioningthatChong[4]considersanAR(1)modelwithastructuralbreakintheARparameterβatanunknowntimek0.Thatis,yt=β1yt−1I{t≤k0}+β2yt−1I{t>k0}+εt,t=1,2,···,T,(0.1)whereI{·}denotestheindicatorfunction.Byimposingsomeregularityconditionsontherandomvariablesy0andεt,a

8、ndtheunknownbreakfractionτ0=k0/T,theasymptotictheory,includingtheconsistenciesandlimitingdistributionsofthelea