In Marcos Lopez De Prado's book, Advances in Financial Machine Learning, the author explains the method of fractional differentiation as an alternative to calculate returns.

The method basically applies a weighted sum to each price, with the motivation of preserving memory (which integer differentiation, such as log returns, does not preserve), and to create a stationary series.

In the book, the author only applies the method to Futures contracts.

I have 2 questions

Can fractional derivatives:

  1. Be applied to any / all other asset classes (equities, cryptos, fx)?
  2. Be applied to Volume Weighted Average Price (VWAP)?

From studying the book, I could not find anywhere where the author gave any conditions on which asset class it should be used on; however he only applied it to Futures. I think the answer to 1. is yes, because really the method is just another way of calculating returns.

But I am unsure if it makes sense to calculate returns using fractional derivatives on a VWAP series.


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