On Estimating Time Series Parameters Using Sample Autocorrelations
利用样本自相关估计时间序列参数
SUMMARY Consider a scalar linear process {xt} whose spectral density is σ 2 k(λ, θ 0) where σ2 is the innovation variance and k(⋅,θ0)∈{k(⋅,θ):θ∈S⊂ℝq}. We introduce a class of estimators of θ0 based only on the sample autocorrelations. These estimators are shown to be consistent and asymptotically normally distributed with a covariance matrix which is independent of the distributions of the innovations. A lower bound to the asymptotic covariances of these estimators is…