Consider i.i.d. with . Now define
Notice that is independent from and from individually. However the three variables are not jointly independent.
Now consider a sequence uch that each triplet has the same distribution as and all these triplets are independent.
With this one has that all have the same distribution as , so that the process is 1 stationary. Also, all pairs with are independent and hence have the same distribution (this gives 2 stationarity). However the triplet has a different distribution from (in fact, and are jointly independent).