一类不可观测ARMA过程参数的最小方差估计的强相容性

Strong consistence of minimum variance estimation of parameters in an unobservable ARMA process

本文讨论一类不可观测ＡＲＭＡ过程｛ｕ１｝参数的估计，基于Ｎ个可观测的样本值ｘ１，ｘ２，……，ｘＮ，其中ｘｔ＝ｕｔ＋δｔ，１≤ｔ≤Ｎ，假设｛δｔ｝满足另一个ＡＲＭＡ方程，我们给出参数的最小方差估计量，并证明了这些估计量的强相容性。

This paper discusses the estimation of parameters of an unobservable ARMA process {ut}, on the basis of samples with N observables: x1, x2, ……,xN, where xt =ut+δt and 1≤t≤N, on the assumption that {δt} is satisfied by another ARMA pro- cess. We give the minimum variance estimators and then prove the strong consistence of these estimators.