alt Hacker NewsI think there's a close linkage between "predictable" and "stationary". Ultimately, if you strip everything away, either there's a core where the future looks like the past (which is equivalent to being stationary), or there isn't. That core could be "the laws of physics and base conditions are stationary", and everything else is deterministic functions applied on top, but the fundamental process is trying to find that stationary core.
In the finance space, the stationary core is often some 'stylized fact' that you're hypothesizing will hold true. This could be e.g., the momentum factor, that if you strip away the noise, there's an underlying trend that will hold over an extended duration.
That's a bit of a vacuous statement. Stationarity makes sample statistics meaningful due to the LLN, sure, but almost nothing is stationary (and even if something is, there is no way to know anyway, you can only assume). If you condition on enough variables and do enough transformations you may get something seemingly stationary and therefore trivially predictable. But all the practical complexity is in that structure you need to specify. The true prediction "problem", when people work on such "problems", really is in the stuff besides the thing that you can just use averages to predict.