[gbrown]

The point is, statistical prediction is definitely a thing, and is not "mathematically invalid" - it's mathematically well defined, with predictable consequences (increasing variance as the extrapolation becomes greater). Certainly, statistical models are not Crystal balls, but they never claimed to be. If you have a reasonable frequentist model and good data about an ongoing process, you should be able to make predictions with reasonable confidence bounds. If you have a reasonable Bayesian model and good data about an ongoing process, you should be able to coherently quantify your uncertainty about the future state of the system.

Obviously, this is more or less feasible in practice, depending on the phenomenon under study. Calling markets unpredictable is not evidence against the existence of rigorous frameworks for statistical prediction.

Don't let bad experiences with inexperienced and overconfident practitioners blind you to established, uncontroversial, mathematical truths.