一类正值线性过程的参数估计

在研究水质污染问题时,文[1]提出了非负一阶自回归模型:X_t=(?)X_(t-1)+ξ_t,其中{ξ_t}为独立同分布非负随机序列,0<(?)<1.此模型中 X_t 表示在时刻 t 时净化池中的污水量,1-(?)_1表示在单位时间间隔内被净化污水的比例,ξ_t 表示在时刻 t 注入净化池中的污水量.文[1]给出了模型参数的极为简便的强相合估计和相应的模拟结果.文[2]把[1]的结果推广到二阶自回归情形,克服了本质上的困难获得相应的结果.本文提出一类更为广泛的正值线性模型     

THE STRONG LAW OF LARGE NUMBER AND PARAMETER ESTIMATION OF ONE CLASS OF NON-NEGATIVE INTEGER-VALUED TIME SERIES

1.IntroductionLet{xt}beatimeseriesdefinedonprobabilityspace{fi,F,P),satisfyingwhere(1)p(t,s,j)isarandomfieldwithValueIor0,t,8EI={0,11,f2,'.},jEN={1,2,'.},andsatisfies(i)p{p(t,s,j)=0}=1whens>t;(1.2)(if)ac(tl,sl,jl)andp(tz,sa,j~)aremutuallyindependentwhenif/iZor81/s2;(ill)FOrfords,j,p(t,s,i)fort2sisanonhomogeneousMarkovChainwithtransitionprobabilityandinitialdistributiont=0T=0(2){Mt}isani.i.d.non-negativeinteger-valuedtimeseriesandindependentofn(t,sli).Inthefollowing,weassumeEMtz相似文献   

THE STATIONALRITY ANDSPECTRAL REPRESENTATION OFONE CLASS OF NON-NEGATIVEINTEGER-VALUED TIME SERIES

1.IntroductionLet{x,}beatimeseriesdefinedonprobabilityspace(fi,r,P),satisfyingwhere(1)ac(t,s,j)isarandomfieldwithvalue1or0,t,sEI={0,FI,12,'.},jeN{1,2,'.},andsatisfies(i)p{ry(t,s,j)=0}=1whens>t;(l'2)(n)ac(tl,sltif)andn(t2,s2,j2)aremutuallyindependentwhenif/jZorsl/s2;(iii)Forfixeds,i,n(t,s,i)fort2sisanonhomogeneousMarkovChainwithtransitionRevisedJune23,1997.tNowworkinginU.S.A.frominstituteofSystemsScience,theChineseAcademyofSciences,Beijing100080,China.probabilityandinitialdistribution…