I have a quick question.
Currently I study daily OHLCVs of some stocks and find that many of them have the Hurst exponent not being equal to 0.5. I know that if it is less than 0.5 then it is a mean reverting series, if more than then it is a trending series. But my question is if $H$ $\neq$ $0.5$ then it is a series containing some memory, should I fractionally differentiate the original price series and work with the new, differentiated, series, for example, for the next day price movement prediction?
I worked through the formula of fractional differentiation and, indeed, found that when we use lags between 0 and 1, we assign some weights to previous prices so that some "info" about them can be included in current price.
I mean, it seems quite legit for me but I do not see much formal research going on using these principles while there are many stocks where the Hurst exponent indicates that they are not random walks (at least, in my sample). Are there any theoretical issues with the HE?
Would be really happy if you can guide on these questions and provide some sources to read!