Variance of partial sums of stationary sequences

Let X1,X2,. be a centred sequence of weakly stationary random variables with spectral measure F and partial sums Sn=X1+.+Xn. We show that var(Sn) is regularly varying of index . at infinity, if and only if G(x):=.x.xF(dx) is regularly varying of index 2.. at the origin (0<.<2).