白噪声谱估计函数的重对数律

LIL FOR THE SPECTRAL ESTIMATE OF WHITE NOISE

设{ε(n),n≥1}为零均值,方差为1的平稳序列,

As another property of spectral estimate like, that of [2], the result of this essayis concerned with the strong consistency of spectral estimate of a certain type ofstationary processes. It reads as follows: For the spectral estimate of F(λ),where ε(1), ε(2),...,ε(N) are observations of the white noise {ε(n), n≥1}, ifEε(1)=0, Eε~2(1)=1, Eε~8(1)<+∞, thenwhereu_4=Eε~2(1)-3.