平稳序列谱函数积分谱窗估计的渐近性态(Ⅰ)

ASYMPTOTIC BEHAVIER FOR INTEGRAL SPECTROGRAPH ESTIMATOR OF SPECTRAL FUNCTION OF A STATIONARY TIME SERIES(Ⅰ)

用积分周期图估计平稳序列的谱函数,无论对于正态的平稳序列还是非正态平稳序列都被证明具有优良的渐近性质。许重光用拟合自回归谱密度估计量 (x)的积分估计谱函数,也证明了此估计量具有优良的渐近性质。本文采用积分谱窗估计量估计谱函数,无论是Gauss序列还是非Gauss序列,都证明了其估计误差过程ζ_N(λ)= (F_N(λ)-F(λ))

To estimate the spectral function of a stationary time series using integral periodogram,The esti- mator's error process weakly converges to a Gaussian process in space C(0,л),either Gaussian or non- Gaussian time series.Xu Cheng guang estimates the spectral function using another algorithm called integral autoregressive spectral estimate,The same result is also obtained. In this paper,The auther presents the integral spectrograph estimator to estinate spectral function of a stationary time series,Like the integral periodogram,The estimator's error process weakly con- verges to a Gaussian Process in space C(0,л)also either for Gauss ian or non-Gaussian time series.