I know you know that and were just simplifying. Just wanted this fact to be better known for practitioners. Your comment on multiplicative processes is spot on.
Absolutely. The effect of straightforward correlations is a change in the variance, which can be measured in finance.
The effect of the nonlinear changing correlations is that future global behavior can't be predicted from local observations without a very sophisticated model.
https://en.wikipedia.org/wiki/Central_limit_theorem#Dependen...
I know you know that and were just simplifying. Just wanted this fact to be better known for practitioners. Your comment on multiplicative processes is spot on.
I say more here
https://news.ycombinator.com/item?id=47437152
It's bit of a shame that these other limiting distributions are not as tractable as the Gaussian.