We know that Wide-Sense Stationary (WSS) process passing through a stable LTI outputs a WSS process.
The stability condition is that the sum of coefficients of the LTI doesn't diverge, and that the double sum over the product of any pair of coefficients also doesn't diverge.
Proof: say $Y[n]$ is the output of an LTI system after inputing the process $X[n]$, then we can find coefficients $\{h\}_i$ such that $$Y[n] = \sum h_i X[n-i]$$
$$E(Y[n]) = E(\sum_i h_i X[n-i]) = \sum_i h_i E(X[n-i]) = (\sum_i h_i) \mu_X$$ $$R_Y(n, n+k) = E\left((\sum_i h_i X[n-i])(\sum_j h_j X[n+k-j])\right) = \sum_i \sum_j h_i h_j E\left(X[n-i] X[n+k-j])\right) = \sum_i \sum_j h_i h_j R_X(k+j-i)$$
Can this proof be extended thus to any higher order moment (with proper stability limitation), thus showing the statement is true for SSS as well?