一类线性平稳序列的谱识别

ON THE SPECTRAL STATISTICAL IDENTIFICATION ABOUT A CLASS OF LINEAR STATIONARY TIME SERIES

本文研究四阶矩存在的鞅差序列所构成的平稳序列的谱函数的识别问题,在文《线性平稳序列积分周期的渐近误差的谱表示》(刘学圃衡阳师专学报1991年第6期)的基础上,进一步证明了其谱估计的误差过程在空间C(o,π)上弱收敛于一个高斯过程η(λ):

In this paper, we devoted to the statistical identificating problems about the spectral function of a class of time series. Under the base of Author's another paper, we have proved that the error process of spectral function estimator η_V(λ)=N^(1/2)(F_N (λ)—F (λ) weakly convergences to aGaussian process, η (λ) with E_η (λ) =0, and in the space C (0. π). In other words, any finite continous functional of η_N (A) have had the same distribution function as Gaussian process η(λ)does. Especially, when μ<3σ~4, the confidence band of the spectral distribution function F (λ) with confidence coefficient Δ (α): have obtained.