Apologies on the unfinished lines in my previous comment. The correction lines below:

"That said, what one can posit is that returns are ergodic. However, ergodicity is very difficult to prove for dynamic systems, of which the financial world is most certainly one. Another confounding factor is that ergodicity is most usually associated with systems in statistical mechanics, where one's scale of observations is close to Avogadro's constant (6.023 x 10^23!), rather than only 13000 returns.