Consider a strictly stationary process $X_t$, $t\in\mathbb{Z}_{\geq 1}$. Could you help me to disprove the following statement:
"For $t, s > 0$, the bivariate vectors $(X_s, X_t)$ and $(X_t, X_s)$ have the same distribution."
I think the statement is false in general but true for Gaussian processes. Can we find a counter-example which proves that the statement is false?