摘要
Consider the model Y_t=βY_t-1+g(Y_(t-2))+ε_t for 3<=t<=T.Here g is an unknown function,βis an unknown parameter,ε_t are i.i.d,random errors with mean 0 and varianceσ~2 and the fourth momentα_4,andε_t are independent of Y_s for all t>=3 and s=1,2. Pseudo-LS estimators■_T^2,■4T and■_T^2 ofσ~s,α_4 and Var(ε_3~2)are respectively constructed based on piecewise polynomial approximator of g.The weak consistency of■4T and■_T^2 are proved.The asymptotic normality of■_T^2 is given,i.e.T^(1/2)(■_T^2-σ~2)/■_T converges in distribution to N(0,1).The result can be used to establish large sample interval estimates ofσ~2 or to make large sample tests forσ~2.
Consider the model Yt = βYt-1+g(Yt-2)+εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var(ε2↑3) are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T(σ2T -σ^2)/DT converges indistribution to N(0, 1). The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.
基金
Supported by the National Natural Science Foundation of China(60375003)
Supported by the Chinese Aviation Foundation(03153059)
关键词
渐近性常态
假LS估计器
误差方差
线性自回归模型
partly linear autoregressive model
error variance
piecewise polynomial
pseudo-LS estimation
weak consistency
asymptotic normality