Given X_n=λY_n+(1-λ) X_(n-1)+(Y_n-Y_(n-1) ), considering the points Y_(n+1), Y_n, Y_(n-1) and then choosing two at random and taking the average?
(Y_(n+1) - Y_n, Y_n-Y_(n-1), Y_(n+1)- Y_(n-1) )
Therefore if X_n=(1-λ)X_(n-1)+ λ Y_n+[((Y_(n+1)-Y_n )+(Y_n-Y_(n-1) )+(Y_(n+1)-Y_(n-1) ))/3] is an auto correlated process, with observations mean (muu) and variance (sigma-square), is there any theorem or lemma that could lead to the derivation of the variance with constant mean (muu)? Useful idea is much appreciated.
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