方差无穷非线性自回归序列的自加权L_1估计

Self-weighted L_1-estimator for infinite variance nonlinear autoregressive model

对具有无穷方差的非线性自回归序列x_t=φ(x_(t-1),x_(t-2),…,x_(t-p),θ)+ε_t,E(ε_t^2)=∞,利用局部二次近似和连续函数空间C(R^q)上弱收敛随机过程最小点的渐近性质,证明了若存在δ≥1,使得E|ε_t|~δ<∞成立,则θ满足一定条件的自加权L_1估计θ_(L_1)是渐近正态估计,Wald检验统计量也具有通常的x^2分布,为模型的统计推断提供了理论基础.

For the nonlinear autoregressive time series model x_t=φ(x_(t-1),x_(t-2),…,x_(t-p))+ε_t with E(ε_t^2)=∞,it is showed that if there existsδ≥1 such that E|ε|~δ<∞,then the distribution ofθ_(L_1),the self-weighted L_1-estimator ofθ,is asymptotically normal and the Wald test statistic has the ordinary X^2 distribution.The local quadratic approximation and the asymptotics for the minimisers of stochastic process defined on C(R^q) are involved in the proof of theorems.