Question regarding exchangeable sequence of random variable I have a question regarding the exchangeable random variable
consider ($x_{m}$) be a (infinite) sequence of random variable, if ($x_{m}$) is stationary, does it implies that ($x_{m}$) is exchangeable? 
There is no reference for this result, so I am wondering it should have a counterexample, but I can not make up one
any help will be extremely appreciated!!

Of course not. Assume that every $x_m$ is uniform on $\{1,2,3\}$ and that $x_{m+1}=x_m+1\pmod{3}$ for every $m$, then the distributions of $(x_m,x_{m+1})$ and $(x_{m+1},x_m)$ are mutually singular hence $(x_m)_m$ is stationary and not exchangeable.
