A common strategy in trading is to use a bollinger band system. Simply put, we bet on reversion to the mean and take the opposite trade to the current movement under the assumption a move is overdone.
However implicit in this is the idea of standard deviation which really only applies to symmetrical distributions. Generally, stocks, futures, etc have long tails. So it would seem regardless this strategy would likely fail any serious scrutiny outside of pairs trading.
We can take the log return of the price series. If returns are distributed log normally then log returns are distributed normally. Suppose this series passes the ADF test with p < 0.01, and a hurst exponent test reveals mild mean reversion properties (0.45 <= H < 0.5).
I've searched and searched and I have not found any information regarding trading this series. Since no one has written about it, it seems like I'm walking into a waste of time. Why couldn't we apply a simple bollinger band strategy to the log return series (rolling) and trade this instead of the price? In the case of "higher frequency data", for example 15 minutes or less, in a highly liquid market it would seem this would have some value.