Given a strictly stationary sequence {Xk, k = …, −1,0,1, …} of r.v.'s one defines for n = 1, 2, 3 …, 
. Here an example of {Xk } is given with finite second moments, for which Var(X 1 + … + Xn )→∞ and ρ n → 0 as n→∞, but (X 1 + … + Xn ) fails to be asymptotically normal; instead there is partial attraction to non-stable limit laws.