On a simplified method of the estimation of the correlogram for a stationary Gaussian process. III.
Mituaki Huzii · Kodai Mathematical Journal · 1966
In this paper we shall deal with a simplified method for the estimation of the correlogram for a stationary process.Let X(n) be a real-valued stationary process with discrete time parameter n.We assume EX(ri)=0.We put 77 1 "V/ ΛΛ \2 2 27* W/IΛ\ WΛ/I I 7*\ 2 tLΛXfl) =(J , £SA(^7,)A(72-r/Z) - 0, y=0, y<0.The new estimate is Σ Mn) sgn (X(n+h))This new estimate Γ h may be considered as follows.We make a nonlinear operation on the input X(n) and assume that the output is Y(ή)=$gn(X(ή)).Then, the estimate Γ h consists of the cross-correlation of the input X(ή) and the output We shall show below that when X(ή) is a Gaussian process satisfying some conditions, the estimate Γ h is an asymptotically unbiased estimate of the correlogram