[WhatDoYouThink?]

If you assumption is it's a dice roll..then there is nothing to discover. However that is the question we are trying to answer...rather than the starting point.

You cannot prove non-stationarity using traditional techniques that cannot cannot uncover and discover anything.

Anyway Renaissance Tech returns tells us there are patterns to uncover.

aiya I din say it's dice roll aka random walk. I only said the data are non-stationary. 

I aso never say there's no pattern. in fact market fractals, which are recurring geometrical patterns for determining market turning pts and directions are quite promising