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While all true, I think variables with infinite variance are hard to come by. For a start, almost everything in the real world is kind of bounded (markets can't

While all true, I think variables with infinite variance are hard to come by. For a start, almost everything in the real world is kind of bounded (markets can't go below zero and also can't jump by more than a certain amount per day either, laws of physics determine min and max weight of people etc). But it's true that CLT requires some form of IID distribution, or something slightly weaker, and that often doesn't apply.

fjkdlsjflkds 3y ago
> markets can't go below zero and also can't jump by more than a certain amount per day either It depends on what you are looking at, and how you are modelling it, isn't it? For example: the value of log(asset_value_today/asset_value_yesterday) can become unbounded (and, thus, so can all its moments). Furthermore, the problem is not just the "finite variance assumption", but the fact that the CLT only talks about what happens asymptotically: for some reason people use t-scores in practice, rather than z-scores. CLT does not imply normality of (e.g.) sum-based estimators if you have finite number of samples (which is pretty much always the case).